At a Glance - 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:
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:
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.
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.
The dimensions of the large outside rectangle are:
So, the area of the larger rectangle is .
This amount includes the area of the pool, which we would not want to have decking. So, subtract out the area of the pool().
The amount of decking we need is : !
Find the area of this shape:
The radius of the circle is 4 cm. Find the area of the yellow section without the equilateral triangle.
A square garden 10 feet long needs to be surrounded by a walk 2 feet wide on only three of its sides. What is the area of the walk?