Area of Simple Shapes

architects floors pic colors
Image Source: http://rackcdn.com

Perimeter is the distance around the outside of an object, but Area is the amount of space inside a two dimensional flat object.

In this post we look at the area of geometric shapes. However we do not look at Compound Areas or Circles, as these will be covered in other posts.

Areas are Important for Surveyors, Town Planners, and Councils.

pic of town planning in color
Image Source: http://clcreport.files.wordpress.com


Aeronautical Engineers work out the areas of aircraft wings when investigating aerodynamic properties and designs.

NASA aircraft calcs diagram
Image Source: http://www.grc.nasa.gov

Area is also very important for Builders, when quoting for costs of materials.

Brick wall subtracting windows
Image Source: http://www.ebricksolutions.com

People who work with lighting and media projectors need to understand the mathematics involved with the dispersion and intensity of light.

inverse light area law
Image Source: http://www.sciencebuddies.org

Now that we know how important Area is to our everyday lives, let’s start looking at the Mathematics of calculating areas.

Here is a great music video to watch all about Perimeter and Area.

Different shapes have different area formulas.

Area of a Rectangle

A very simple shape is the “Rectangle”.

A Rectangle has an Area of Base x Height, which is sometimes called Length x Width, or Length x Height.

A = b xh diagram
Image Source: http://www.k6-geometric-shapes.com

We can prove this formula by drawing a whole bunch of rectangles, and counting how many squares are inside them.

pics of rectangles on grid paper
Image Source: http://www.geom.uiuc.edu

However, not all shapes are as simple as a Rectangle. If we push a Rectangle sideways, we from a Parallelogram.

Area of a Parallelogram

The Area of a Parallelogram is Area = base x height

Here is a video all about the Area of a Parallelogram.

How do you like this for a real life Parallelogram!

Parallelogram Building at Port
Image Source: http://www.elec-intro.com

Area of a Triangle

We could work out the area of a triangle by drawing it to scale on grid paper and counting squares.

Area of triangles by Counting Squares
Image Source: http://www.geom.uiuc.edu

But it is much easier to measure the triangle’s base and height, and use a mathematical formula to calculate the area.

This formula can be worked out very easily, because a Triangle is half of a Parallelogram.

Area of any Parallelogram is Area = base x height.

So the area of any Triangle is : Area = 1/2 x base x height.

Here is a video that explains how this works.

Here is an example of how we calculate the area of a triangle.

triangle example working out
Image Source: http://www.loisterms.com

Note that the above example used “FISC” working out steps.

Formula
Information diagram
Substitution of values into Formula
Calculate the final answer and make sure it has square units on it. Eg. sq cm, sq inches, sq km, and so on.

It is vitally important to always show these steps when calculating the area of any shape.

Area of a Trapezium (or Trapezoid).

This shape is a bit like a Parallelogram, except that it only has two parallel sides.
Australians call it a “Trapezium”, and Americans call it a “Trapezoid”.

Trapezium Area Diagram
Image Source: http://www.mathwarehouse.com

Here is a quick little video to help remember how to calculate the area of a Trapezium.

Area of a Rhombus

A Rhombus is a Parallelogram that has all four sides equal. We can work out its area using Base x Height, but we can also work out the same area by multiplying the two internal diagonals together, and dividing by 2.

Rhombus diagram + examples
Image Source: http://www.thefreemathtutor.com

Answers to Rhombus Questions:
Q1. 418 sq cm, 41600 sq mm, 0.0006 sq m.
Q2. 91 sq cm
Q3. (1000×2) / 10 = 200mm.
Q4. (120×2) / 30 = 8m.

Area of a Kite

A Kite is a similar shape to a Rhombus, and its area is obtained by multiplying together its diagonals.

diagram of kite and formula
Image Source: http://www.coolmath.com

Summary of Area Formulas

Here is a set of formulas that are used in mathematics for finding areas.

Area and Perimeter Formulas in color
Image Source: http://www.math-videos-online.com

Nasa area formulas
Image Source: http://www.grc.nasa.gov

Online Activities

Here is an Online learning Activity to do that is all about Perimeter and Area

Pic Link to Perim Area Activity

http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/perimeter_and_area/index.html

Here is an activity on Areas of Rectangles, Triangles, and Parallelograms.

(This one takes a little while to load up).

Link to BBC Areas Activity

Click the question mark to enter your answer, then click the ok to check your answer.

http://www.bbc.co.uk/schools/ks3bitesize/maths/measures/area/activity.shtml

Online Area and Perimeter Games

Play this fun game where we use basic Area and Perimeter skills to design zoo enclosures for animal exhibits:

Pic Link to Zoo Game

http://www.mrnussbaum.com/zoo/index.html

Play this interesting game to find the relationship between Perimeter and Area.

Image Link to Game

http://pbskids.org/cyberchase/games/perimeterarea/index.html

Have some fun learning about irregular shaped areas with this Tangrams game.

Link to Tangrams Game

http://pbskids.org/cyberchase/games/area/index.html

A Challenging Area and Perimeter Game

Perim and Area Party Tables

It is necessary to get right on the corners of the initial symbols, get the hand symbol, and then drag the items around the grid to make them fit according to the Perimeter and Area rules given.

Note that final areas of items are not allowed to overlap. However, it might be necessary to do some overlapping while making the shapes.

http://www.mathplayground.com/PartyDesigner/PartyDesigner.html

Test Yourself Online

Click the link below for an Online Lesson on Area of Triangles, and scroll down the page to do a five question online test.

http://www.mathgoodies.com/lessons/vol1/area_triangle.html

Click the link below for an Online Lesson on Area of Parallelograms, and a five question online test.

http://www.mathgoodies.com/lessons/vol1/area_parallelogram.html

Click the link below for an Online Lesson on Area of Trapeziums, and a five question online test.

http://www.mathgoodies.com/lessons/vol1/area_trapezoid.html

Here is an Online Quiz on Areas of Rectangles and Parallelograms, that includes finding unknown sides, if Area is known.

http://au.ixl.com/math/year-7/area-of-rectangles-and-parallelograms

Try these mixed practice questions on Perimeter and Area.

http://www.mathgoodies.com/lessons/vol1/practice_unit1.html

Here is one final set of mixed problems.

http://www.bbc.co.uk/scotland/learning/bitesize/standard/maths_i/measure/quiz/area_general/

Hope this has covered all areas !

Related Items

Perimeter
Circumference
Area of a Circle
Interesting Circles
Composite Areas
Measurement Formulas
Tall Buildings and Huge Water Dam
My Virtual Home

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