Study Guide

How to Find the Area of Irregular Shapes

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Area of Irregular Shapes

In real life figures are often irregular shapes - a little bit messy. Think of your messy bedroom once more ‐ is it a perfect rectangle?

The trick: break these figures into shapes that you know well (and whose area you know how to find).

1. Find the area of this room:

3- 2 -4 -6 irregular shape

This can be done in two different ways:

Method #1 Method #2
Divide the figure into two rectangles and find all missing lengths.

The larger rectangle has an area of

The smaller rectangle has an area of

If we combine these we will find the total area:
Draw two lines to make the figure into one large rectangle.

The area of the large rectangle is

However, a rectangle is not included in our original figure, so we need to take out the area of the white rectangle

2. Find the area of this portion of a basketball court:

basketball court with rectangle 12 by 19 and diameter 12 circle

This figure is already divided into two shapes: a rectangle and half a circle.

We need to find the area of each and add them together.

12 x 19 = 228

area of half circle = 1/2 pi r^2 = 56.62 ft^2

3. A 20 foot x 12 foot pool is to be surrounded by a deck 6 feet in width. How many square feet of decking is needed to do this?

As always, we want to draw a picture of what this looks like.

20 by 12 pool

The dimensions of the large outside rectangle are:

width = 6 + 12 + 6 = 24

length = 6 + 20 + 6 = 32

So, the area of the larger rectangle is 24 ft x 32 ft = 768 ft ^2.

This amount includes the area of the pool, which we would not want to have decking. So, subtract out the area of the pool(20 x 12 = 240 ft^2).

The amount of decking we need is : 768- 240 = 528 ft^2!

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