Passy's World of Mathematics

Volume of Prisms

Posted on May 3, 2013 by Passy

Image Source: http://img.thesun.co.uk

Many jobs require a good knowledge and understanding of Volume.

Medical Personnel need to administer blood and drugs in specific volumes to patients using cylindrical injection containers and intravenous drips.

Concreters need to calculate correct volumes of material required, because concrete is expensive, and it is hard to dispose of any extra left over material.

Heating and Cooling Technicians need to calculate volumes of buildings to work out what types of systems to install.

Hairdressers need to mix chemicals together in the correct volumes when making hair treatments.

Bakers and Chefs need to measure out volumes of ingredients accurately, and know how to scale these amounts up and down for making different quantities of product.

People designing and building cars need to make sure there is enough volume inside the car for occupants and their belongings to be transported comfortably and safely, as well as ensuring the volume is correct for air bags to deploy effectively during accidents.

Water authorities in cities need to make sure that there is an adequate volume of water held in dams and reservoirs.

Definition of Volume

The Volume of a 3D Shape is the number of cubes needed to fill the inside of the shape.

In mathematics we call the 3D shape a “Prism”.

A 1cm cube is about the same size as a sugar cube.

Using some simple 3D box shapes, we can investigate Volume relationships as shown in the following examples:

From our investigation, we can see that the volume of a 3D box shape, (called a “Rectangular Prism”), is always the LENGTH x WIDTH x HEIGHT

or the Area of the bottom layer multiplied by how many stacks high the prism is.

This means that we can use the mathematical formula of V = L x W x H, (rather than drawing and counting cubes), to work out the volume of any Rectangular Prism.

The following video shows the cubes stacking concept for working out the formula for Rectangular Prism volume

Volume of Rectangular Prisms

The following example shows how to calculate the volume of a box shape Rectangular Prism.

Volume of Prisms – General Formula

Mathematicians have found that for any shape Prism that has two identical ends, the Volume is always the Area of the End multiplied by how long or high the prism is.

Note that when the Prism is layed on its side (like the examples above), we still call the length between the identical ends the “Height”.

This is a bit confusing. Just remember that the standard position for a cylinder (or any of these Prisms), is standing up straight like a Coca Cola can, or a tin of fruit at the supermarket, and not lying on its side.

Area Formulas that we need to use for Prism ends are the following:

Volume of a Triangular Prism

For a prism which has triangle shaped ends, we need to first find the area of the triangle using A = 1/2 x base x height of triangle.

Once we have this area, we can then multiply it by how high (or how long for sideways prisms).

Eg. V = A x H gives us the Volume of the prism.

This is shown in the following example.

The following video shows how to calculate the Volume of Triangular Prism.

Volume of Trapezoid Prism

For a prism which has Trapezium shaped ends, we need to first find the area of the Trapezium using A = 1/2 (top + bottom) x height of trapezium.

Once we have this area, we can then multiply it by how high (or how long for sideways prisms).

Eg. V = A x H gives us the Volume of the prism.

This is shown in the following example.

Volume of a Cylinder

For a prism which has Circle shaped ends, we need to first find the area of the Circle by Pi x Radius x Radius.

MAKE SURE THAT IF THE DIAMETER ALL THE WAY ACROSS THE CIRCLE IS GIVEN ON THE DIAGRAM, THAT YOU DIVIDE THIS DIAMETER BY 2 TO GET THE RADIUS !

Once we have this area, we can then multiply it by how high (or how long for sideways prisms).

Eg. V = A x H gives us the Volume of the cylindrical prism.

This is shown in the following example.

Volume of an Irregular Prism

Sometimes the ends of our prism are not a simple shape like a Rectangle, Square, Triangle, Trapezium, or Circle.

This means that we cannot easily calculate the area of this odd shaped end.

For these types of prisms, the area is usually given to us in the question, and we then use this area for our V = A x H calculation.

This is shown in the following example.

However, sometime we can use “Composite Areas” method to calculate the irregular area end of the Prism.

If you are not sure about what “Composite Areas” are, then take a look at our Composite Areas lesson at the link below:

http://passyworldofmathematics.com/composite-areas/

The following video shows how to do a composite areas volume calculation for an irregular “L-shaped” prism.

Volume of Prisms Formulas

For Rectangular, Triangular, and Cylindrical Prisms, we can do calculations faster by using “all in one” formulas, where the Area x Height calculation has been combined together to give a single volume formula for the 3D shape.

The following are the “all in one” formulas we can use.

Volume of Rectangular Prism Using Formula Method

The following example shows how to use the “all in one” volume formula for a Rectangular Prism.

Volume of Triangular Prism Using Formula Method

The following example shows how to use the “all in one” volume formula for a Triangular Prism.

Volume of a Cylinder Using Formula Method

The following example shows how to use the “all in one” volume formula for a Cylindrical Prism.

The following video shows how to calculate the Volume of a Cylinder using the Formula Method.

This next video shows how to do a practical problem about a cylindrical storage tank.

Shown in the next video is how to ESTIMATE the volume of a cylinder if you don’t have a calculator with the exact pi value on it, and you do not want to use Pi = 3.1416 and do a difficult decimal multipication by hand.

This technique is also useful for quickly checking an answer, or for eliminating unlikely letter options on a multiple choice question.

Volume and Capacity

If we have a container filled with liquid or gas,the Volume is specified in “Capacity” units.

Capacity units are Millilitres (mL), Litres (L), Kilolitres (kL) and Megalitres (ML).

This means for Liquids and Gases in containers, we do not specify their volume in cubic centimetres or cubic meters.

The container they are in is a solid structure with Volume units of cubic centimetres or cubic meters, but the liquid or gas occupying the container has a Volume that is specified in Millilitres, or Litres.

Eg. Volume is how big the container is, but Capacity is how much the container can hold.

Container size is specified in cm or m cubed, but how much liquid or gas is in the container is specified in mL or L.

As a typical example of a “Capacity” type Volume, consider a standard 375ml can of Coca Cola.

MegaLitres (ML) are a very large unit of Volume that is most commonly used to specify the Volume of Water contained in large Dams and Resevoirs.

One MegaLitre = 1 million Litres.

The following Conversion Diagram can be used for converting Capacity Units.

Metric VOLUME and Capacity Converter

The following web page has an easy to use online metric VOLUME and CAPACITY converter.

http://www.onlineconversion.com/volume.htm

Volume in the Real World

Image Source: http://alkispapadopoulos.com

It can be seen in the above photo that we have a rectangular prism shaped Trench, containing a cylindrical shaped Pipe.

Cement is delivered in cubic meters, and the workers would need to have calculated how much cement needed to be delivered for the job.

In this calculation they would need to have done Rectanglar Trench Volume minus the Volume of the cylinder Pipe.

If they did not do this calculation carefully and correctly, then they would either have too much cement, (which is expensive to dispose of), or not enough cement which could mean that they would not be able to complete the job on time.

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Posted in Circles, Math Applications, Math in the Real World, Measurement, Measurement Formulas | Tagged 3d volume, capacity and liquids, cylinder, cylinder volume, cylindrical prism, how to calculate volume, how to convert capacity, how to do volume, measurement, prism volume, pyramid, real world volume, rectangular prism, rectangular prism volume, triangular prism, triangular prism volume, volume and capacity, volume calculations, volume in the real world, volume of cylinder, volume of liquids, volume of prisms, volume of rectangular prism, volume of triangular prism | Leave a comment

Total Surface Area

Posted on April 28, 2013 by Passy

Image Source: http://www.photl.com

Total Surface Area (“TSA”) is important for Painters, so that they know how much paint will be required for a job.

Engineers, Designers, Scientists, Builders, Concreters, Carpet Layers, and other occupations also use Total Surface Areas as part of their work.

In this lesson we show how to calculate the Total Surface Area of Rectangular and Triangular Prisms, including Cylinders, as well as the TSA of Pyramids.

TSA of Rectangular Prisms

One method of calculating the TSA (Total Surface Area) is to “unfold” a 3D shape, into its flat “2D” net which the shape is made from.

From the above Net, we can see that a Rectangular Prism is made of 3 pairs of Rectangles, which creates a Net containing a total of six rectangles.

To determine the TSA, we need to find the area of all six rectangles, and then add up these areas to find the total area.

The following video shows how to calculate the Volume of a Rectangular Prism by unfolding it into its Net.

TSA Formula For Rectangular Prisms

If we assign Algebra letter values for Length, Width, and Height on a Rectangular Prism, we can work out the following general Formula for the TSA of any Rectangular Prism.

The following Video shows how to derive the above TSA formula for a Rectangular Prism.

TSA of Rectangular Prisms Using the TSA Formula

The following Video shows how to calculate the TSA of a rectangular Prism without using Nets.

If we have the Length, Width, and Height values for a Rectangular Prism, we can calculate its TSA by using the TSA Formula.

This saves us having to draw out the flat 2D Net of the shape.

The following Video shows how to calculate the TSA of a Rectangular Prism using both Nets and the Formula.

This next video goes through a Practical problem about painting a wooden chest.

TSA of Triangular Prisms

Image Source: http://3.bp.blogspot.com

The Toblerone chocolate bar packaging is a classic example of a Triangular Prism.

One method of calculating the TSA (Total Surface Area) is to “unfold” a 3D shape, into its flat “2D” net which the shape is made from.

If we have measurements for our Triangular Prism, then we can calculate the TSA using the shapes on the 2D Net.

TSA Formula For Triangular Prisms

If we assign Algebra letter values for Length, Width, Height, and Sloping Side Leght on a Triangular Prism, we can work out the following Formula for the TSA of a symmetrically shaped Triangular Prism.

The above formula only works for Triangular Prisms which have Isosceles or Equilateral Triangular ends.

The problem with Triangular Prisms, is that we can have triangular ends which are not symmetrical, as shown in the example below.

These irregular triangles do not follow our formula.

Therefore we usually create Nets for all Triangular Prisms and then use the General Approach:

TSA = 2 x Triangle End + Bottom Rectangle + Left Rectangle + Right Rectangle.

Pythagoras Theorem and Triangular Prisms

If we are given a Triangular Prism, with only the side measurements, and we do not have its Height; then we can use Pythagoras Theorem to find the Height.

The following Video (which is in two parts), shows how to use Pythagoras Theorem on Triangular Prisms.

Here is Part 2 of the Video:

TSA of Cylinders

One method of calculating the TSA (Total Surface Area) is to “unfold” a 3D shape, into its flat “2D” net which the shape is made from.

The following video shows how a 3D Cylinder is unwrapped into its 2D Net.

Consider the following Cylindrical Water Tank with a Height of 10m and Radius of 2m.

Working out the Area of the Rectangle involves using the Circumference of the circle which the Rectangle is wrapped around.

TSA Formula For Cylinders

If we assign Algebra letter values for the Radius and Height on a Cylinder, we can work out the following general Formula for the TSA of any Cylinder.

Here at Passy World we find it much easier to use the TSA Formula for solving problems involving Cylinders.

We prefer using the formula to drawing out a Cylinder’s 2D Net and working out the separate shapes from the Net.

TSA of Cylinders Using the TSA Formula

If we have the Radius and Height values for a Cylinder, we can calculate its TSA by using the TSA Formula.

This saves us having to draw out the flat 2D Net of the shape.

TSA of an Open Top Cylinder

The following video shows how to calculate the TSA of a Cylinder which does not have a top on it.

TSA of a Half Cylinder

The following video shows how to calculate the TSA of a Half Cylinder.

TSA of Square Based Pyramid

Pyramids are not Prisms because they do not have a uniform cross section.

However we can still draw nets for them and calculate their TSA.

A 3D Square Egyptian type Pyramid unwraps to a 2D Net that contains one central square, surrounded by four equal triangles.

The following example shows how to calculate the TSA of a Square Pyramid.

TSA Lesson Plan for Teachers

Here at Passy’s World we have found the best way to learn TSA is to first start with the Nets of the 3D Solid Prisms.

The following PDF document contains the Nets for Rectangular Prism, Triangular Prism, and Cylinder.

http://passyworldofmathematics.com/pwmPDFs/NetsofSolids.pdf

Students are given a printed copy of these nets, and for each shape, cut the net out, fold it to see how it makes the 3D shape, but do NOT glue it together.

Instead stick it down flat into their math workbook, with the 3D shape image with it on the same page.

For each shape we then work through a Prism with number values on it, and write the working out of areas directly onto the flat Net.

They then add up all these areas on the Net to get the Total Surface Area.

Later we move on from using nets of Rectangular Prisms and Cylinders, to simply using the mathematical formulas for the TSA of these shapes.

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Posted in Area, Area Formulas, Measurement Formulas | Tagged 2d nets, 3d area, area of cylinder, area of rectangular prism, area of triangular prism, cylinder, cylindrical prism, how to calculate surface area, how to do surface area, net of cylinder, net of rectangular prism, net of triangular prism, nets of prisms, prism area, pyramid, rectangular prism, surface area, surface area of cylinder, surface area of prisms, surface area of rectangular prism, surface area of triangular prism, total surface area, triangular prism, TSA | Leave a comment

Converting Metric Units

Posted on April 26, 2013 by Passy

Image Source: http://www.simplum.com

Many people need to convert Metric Units as part of their job.

People such as Tradesmen, Engineers, Scientists, Construction Workers, Doctors, Pharmacists, Fashion Designers, Interior Decorators, Architects,Builders, Statisticians, Nurses, Firemen, CSI Detectives, and many others.

In this lesson we look at Converting Metric Units of Length, Area, Volume, Capacity, and Mass.

Converting Metric Length

Metric Lengths are in Kilometres (km), Meters (m), Centimetres (cm), and Millimetres (mm).

The following Conversion Chart can be used to convert metric units of Length.

Metric LENGTH Converter

The following web page has an easy to use online metric length converter.

http://www.onlineconversion.com/length_metric.htm

Converting Metric Area

Area units are simply the normal metric lengths squared.

A 1km by 1km square is 1000m x 1000m in size, this means that to convert Km to m AREA, we have to multiply by 1000 x 1000, or 1000 squared.

A 1m by 1m square is 100cm x 100cm in size, this means that to convert m to cm AREA, we have to multiply by 100 x 100, or 100 squared.

A 1cm by 1cm square is 10mm x 10mm in size, this means that to convert cm to mm AREA, we have to multiply by 10 x 10, or 10 squared.

This is shown on the following conversion diagram.

In the Metric System there are special additional Area units for specifying the size of Land.

This unit is called the “Hectare” and is about two and a half Acres in size.

Metric AREA Converter

The following web page has an easy to use online metric AREA converter.

http://www.onlineconversion.com/area.htm

Converting Metric Volume

Volume units are simply the normal metric lengths cubed.

A 1km by 1km by 1km Cube is 1000m x 1000m x 1000m in size, this means that to convert Km to m VOLUME, we have to multiply by 1000 x 1000 x 1000, or 1000 Cubed which is 1000 to the power of three.

A 1m by 1m x 1m Cube is 100cm x 100cm x 100cm in size, this means that to convert m to cm VOLUME, we have to multiply by 100 x 100 x 100, or 100 Cubed which is 100 to the power of three.

A 1cm by 1cm x 1cm Cube is 10mm x 10mm x 10mm in size, this means that to convert cm to mm VOLUME, we have to multiply by 10 x 10 10, or 10 Cubed which is 10 to the power of three.

This is shown on the following conversion diagram.

Volume Conversions often produce very big answers that are in the millions.

This happens simply because it can take a lot of cubes to fill up a 3D space.

Volume and Capacity

If we have a container filled with liquid or gas,the Volume is specified in “Capacity” units.

Capacity units are Millilitres (mL), Litres (L), Kilolitres (kL) and Megalitres (ML).

This means for Liquids and Gases in containers, we do not specify their volume in cubic centimetres or cubic meters.

Eg. Volume is how big the container is, but Capacity is how much the container can hold.

Container size is specified in cm or m cubed, but how much liquid or gas is in the container is specified in mL or L.

As a typical example of a “Capacity” type Volume, consider a standard 375ml can of Coca Cola.

MegaLitres (ML) are a very large unit of Volume that is most commonly used to specify the Volume of Water contained in large Dams and Resevoirs.

One MegaLitre = 1 million Litres.

The following Conversion Diagram can be used for converting Capacity Units.

Metric VOLUME and Capacity Converter

The following web page has an easy to use online metric VOLUME and CAPACITY converter.

http://www.onlineconversion.com/volume.htm

Converting Metric Mass

Image Source: http://db2.stb.s-msn.com

When we measure the weight of objects in the Metric System, the units of mass we use are Tonnes, kilograms, grams, and milligrams.

A typical medium sized car weighs about a Tonne, which is the same as 1000 kilograms.

Medicine pills we take for illness often have many of their active ingredients present in very small amounts of milligrams.

(A milligram is one thousandth of a gram).

For converting Masses, the following chart can be used.

Metric Mass Converter

The following web page has an easy to use online metric MASS converter.

http://www.onlineconversion.com/weight_metric.htm

Ladder Method for Converting Metric Units

An alternative way of converting metric units is to use a method that involves shifting the decimal point.

The number of places that the decimal needs to be shifted depends on the number of “steps” that need to be taken along the ladder diagram to get from the original unit to the desired unit.

An example of using the “Ladder Method” is shown in the following diagram.

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Posted in Measurement, Measurement Formulas | Tagged capacity, capacity units, capacity versus volume, capacty and volume, converting area, converting length, converting mass, Converting Volume, hectare areas, how much is a hectare, how much is one hectare, how to conver volume, how to convert area, how to convert hecatares, how to convert length, how to convert mass, how to convert metric units, length conversion, metric area units, metric conversions, Metric Converter for Area, Metric Converter for Length, Metric Converter for Volume, metric length units, metric mass, Metric Units, metric volume units, what is capacity | 1 Comment

Arc Length and Area of Sectors

Posted on April 19, 2013 by Passy

Image Source: http://www.jeffcoughlin.com

In this lesson we look at the fractions of circles which are called “Sectors”.

We cover how to find the “Arc Length” and the “Area” of these sectors.

This lesson assumes that people already know how to calculate the “Circumference” and the “Area” of a Circle.

If you need to revise Circumference and Area, then take a look at our previous lessons at the following links:

http://passyworldofmathematics.com/circumference/

http://passyworldofmathematics.com/area-of-a-circle/

Definition of a Sector

A sector is a piece of a circle that is cut out along two radiuses (radii).

If it is shaped like a single slice of pizza, it is a “Minor” sector.

Image Source: http://blogspot.com

If the Sector is shaped like a yellow Pacman, then it is a “Major” Sector.

Eg. The large remaining section of Pizza in the above picture is a MAJOR sector, because it is between one half circle and a full circle in size.

Quarter Circles and Half Circles are also “Sectors”.

Sectors should be familiar to anyone who has ever drawn a Pie Chart.

It is important not to confuse “Sectors” with “Segments”, which are a different type of fraction of a full circle.

Sectors in the Real World

Sectors are important for designing and building Freeway exits, when they use a “Clover Leaf” style Interchanges.

Image Source http://www.modot.org

Sectors are also found on hard drives in computers. However these “sectors” are slightly different to the ones we do in Mathematics, as they are actually not a full sector, but part of a math sector that is between two circular “tracks”.

Image Source: http://www.datarecoverylink.com

Arc Length for a Sector

For a sector, we can find how long it’s curved part is, by working out the fraction of a full circle we are dealing with.

The following video explains what a sector is, and how to calculate its Arc Length.

This next video shows three Arc Length examples

Sector Arc Length Example 1

The following example shows how to find the Arc Length of a “Minor” sector.

A Minor Sector is basically a small part of a circle, such as a single piece of Pizza.

Sector Arc Length Example 2

This example shows how to calculate the Arc Length for a “Major” sector.

Area of a Sector

The following video shows how to calculate the Area of a Sector.

The next video also shows how to calculate the Areas of Sectors.

Sector AREA – Example 1

The following example shows how to calculate the AREA contained inside a “Minor” sector.

Sector AREA – Example 2

This example shows how to calculate the AREA for a “Major” sector.

Video on Arc Length and Areas of Circles

The following video provides examples of both Arc Length and Sector Area calculations.

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Donate any amount from $2 upwards through PayPal by clicking the PayPal image below. Thank you!

Enjoy,
Passy

Posted in Area, Area Formulas, Area of Circle, Measurement, Measurement Formulas | Tagged arc length, Arc Length and Area of Sectors, area, calculate arc length, calculate sector area, circle math, circle mathematics, circle maths, circle sector, Circle Sectors and Arcs, circumference, determine sector area, diameter, how to calculate Arc Length and Area of Sectors, how to claculate arc length, how to determine Arc Length and Area of Sectors, how to do Arc Length and Area of Sectors, how to do sector area, radius, sector, sector arc length, sector area, sector length, sectors in circles | Leave a comment

Pythagoras and Right Triangles

Posted on March 14, 2013 by Passy

From the Pyramids to the current day, Mathematics, Measurement, and Geometry have been critical to the success of any building project.

Daniel is a Carpenter friend of Passy’s World, and has been busy making a wall frame and strengthening it using triangulation involving metal strips that are nailed to the back of the wooden frame to keep it straight and give it strength.

The diagonal metal strips and the wall frame verticals form a series of Right Angled Triangles, which give the frame strength and rigidity.

In this lesson we look at a special measuring rule for Right angled triangles.

This rule is called the “Pythagoras Theorem”, because it was invented by a Greek Mathematician whose name was Pythagoras.

The Diagonals Check for Squareness

Let’s say you have just had your favorite picture framed for a wall print.

But when you go to the shop it doesn’t look right; the frame looks crooked.

You can actually proove it is crooked by measuring the diagonals.

The green diagonal is actually slightly longer than the pink diagonal, and so we know for certain the picture frame is crooked.

THE TWO DIAGONALS OF A SQUARE OR RECTANGLE MUST BE EQUAL BECAUSE THESE SHAPES CONTAIN TWO IDENTICAL PYTHAGORAS TRIANGLES WHICH BOTH HAVE THE SAME HYPOTENUSE LENGTH.

This measuring check is a great way to check that Pictures, Doors, Windows, Cupboards, etc have been made properly, and it is regularly used by trades people and builders.

Everyone will probably be able to use this check at some stage in their lives.

Amazing History of the Pythagorean Theorem

The following five minute video gives an amazing history lesson on the Pythagoras Theorem.

The following video is about the Death of Pythagoras.

Pythagoras Rule Explained
Pythagoras was a Greek Mathematician from around 2500 BC, and developed a rule for L-shaped Right Angled Triangles.

The following diagrams show an explanation of this rule.

Pythagoras started with a 90 degree (L-shaped)Right Triangle.

Next he added Squares onto each side of the Triangle:

Then he added Grid Lines to measure the Areas of these squares.

From the values of the Squares he noticed a pattern which is now known as “The Pythagoras Theorem”.

He then tried out this rule on many Right-Angled Triangles, and found that it always works.

Pythagoras Theorem Example

The following example shows how to label a Right Angled Triangle and apply the Pythagoras Rule to it.

Pythagoras and Screen Sizes

Screen sizes are measured diagonally.

This means that a 40 inch screen is actually made of a rectangle that is less than 40 inches wide.

(The screen size measurement is shown by the bright green line in the image below).

This 40 inches specified for the screen is the hypotenuse of a Right Angled Triangle, and so the bottom of screen width, (shown in blue), is part of the “L” in the triangle, and it is shorter than the diagonal 40 inches.

Pythagoras Theorem Videos

The following is a video of a Prezi presentation all about Pythagoras Triangles.

The following video shows several examples of how to work out Pythagoras type mathematics questions.

Here at Passy’s World we are big fans of the game “Halo”, so we just had to include the following video:

Equal Sides of a Square Question

These type of finding sides problems are different to the usual finding sides question.

The following video gives a good explanation of how to do this type of question.

Pythagoras Word Problems Videos

The following videos work through a couple of typical Pythagoras Word Problems

Interactive Pythagoras Online Lesson

The following online lesson from BBC Maths has video instruction as well as a question which can be done on the screen.

http://www.bbc.co.uk/schools/gcsebitesize/maths/geometry/pythagorastheoremact.shtml

Pythagoras Online Wall Wisher Resources

The following Wall Wisher page contains a page of clickable post-it notes that will take you to images, web pages, and videos all about Pythagoras Theorem.

Created with Padlet

To go to our Pythagoras Wall Wisher Resources page full screen, click the following link:

http://padlet.com/wall/Pythagoras9

Pythagoras Millionaire Question

One other place you may use Pythagoras knowledge is on the Millionaire Game Show.

Check out the following video, where not even most of the helper audience do not know the Pythagoras 3, 4, 5 triangle either.

The video is called: “When not knowing Math can cost you $15000”

Pythagoras Game – “Clueboxes”

Double click to open each of the nine clueboxes below.

Solve the problems inside.

Here is an example of what is inside a cluebox:

Each successful solution will supply you with a clue to use in the decoder grid below.

When you have all nine clues, click the link and enter the password.

It will take you to the treasure !

Click the following link to play this fun game:

Pythagoras Clue Boxes Game

Pythagoras Music Videos

The following video contains digital avatars singing about Pythagoras and is very entertaining.

Have a Look and Listen to this sweet jazzy tune, which shows everything you need to know and learn.

This next video is not exactly educational, but it does provide some G-Rated entertainment.

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Posted in Geometry, Jobs that use Geometry, Math Applications, Math in the Real World, Pythagoras | Tagged applications of Pythagoras, find side of triangle, finding hypotenuse of triangle, how to do Pythagoras, how to find unknow side of triangle, how to use Pythagoras, Pythagoras examples, Pythagoras explained, Pythagoras explanation, Pythagoras help, pythagoras history, Pythagoras in building, Pythagoras in the real world, pythagoras music video, Pythagoras rap, Pythagoras Rule, Pythagoras screen size, Pythagoras Theorem, real world pythagoras, right angled triangle, right triangle, triangle math | 7 Comments

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