Area of Irregular Shapes at a Glance

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 ()

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

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 !

What is the area of the shape below? Each of the measures is in inches.
We can find the area of this shape by cutting it up into smaller shapes and finding the areas of each of the smaller shapes. Then we just add 'em up and smoosh 'em back together.
We're given all of the measures of the 3 rectangles we've cut this shape into, except the length of the center rectangle.
We know the length of the dotted line is 7 inches and we know the length of the cut out corner pieces are each 2 inches. So the total length of the center rectangle is 2 + 7 + 2 or 11 inches. The width of 6 inches is already given to us.
Pulling a rabbit out of a rectangular hat is just about as easy as finding the area of each rectangle that makes up this shape. The top and bottom rectangles have an area of 7 in × 2 in = 14 in². The center rectangle has an area of 11 in × 6 in = 66 in².
Adding the area of each of these rectangles up, we get a total area of: 14 + 66 + 14 = 94 in².

Show Next Step

What is the area of the given shape?
This looks like a graham cracker and an orange slice stuck together, or a box with half a ball on top, or maybe a basketball court. Whichever way we look at it, it looks like a rectangle and half of a circle.
By splitting this shape up into two shapes, we can find the area of each and then add them together. First, we have to find the missing measures.
The width of the rectangle is 8 ft. but we don't know the length. We do know the radius of the circle is 6 ft.
We can double the radius to find the diameter of the circle, and the diameter of the circle is the same as the length of the rectangle, which is 12 ft.
Now we can find the area of the rectangle and the area of the half-circle. The area of the rectangle is base × height = 8 × 12 = 96 ft².
The area of the half circle is ½ × πr² = ½ × π × 6². So the area of the circle is ½ (3.14)(36) = 56.52 ft².
The total area of the shape, then, is 96 + 56.52 = 152.52 ft².

Show Next Step

What is the area of the shaded donut below?
To find the area of this shape, we need to find the area of the big circle and then subtract the area of the smaller circle.
The area of the larger circle is π (16)² and the area of the smaller circle is π (4)².
By subtracting the smaller area from the larger area, we get the area of the shaded donut, which is a delicious, frosting covered π (16)² – π (4)² = 803.84 – 50.24 = 753.6 ft².