Finding the area of an irregular shape

We know how to find the area of regular shapes such as a triangle, circle, or rectangle. For example, the area of a rectangle is length times width (A = lw).

The problem, however, is that most shapes are not perfect rectangles. If you need to find the area of an irregular shape, split it into regular shapes. For example, find the area of this irregular shape:

In order to find the area of this irregular shape, you must draw a line to divide this into two rectangles. Here are two ways to do that:

     

After dividing the irregular shape into regular shapes, you must determine the dimensions (length and width) of the rectangles.

In the red/green diagram above, the length of the red rectangle is 30 inches and its width is 15 inches. The green rectangle takes a little bit of calculation to determine its dimensions. All the way along the bottom is 35 inches and along the top of the red is 15 of those 35 inches. So the bottom of the green is 20 inches (35 - 15). Likewise, the full height along the red side is 30 inches, and the other side of the red from the green on up is 15 inches. So the height of the green rectangle is 15 inches (30 - 15). Thus the area of the red rectangle is 30 x 15 or 450 in2 and the area of the green rectangle is 20 x 15 or 300 in2. Altogether, the irregular shape is 750 in2 (450 + 300).

In the blue/orange diagram above, the length and width of the orange rectangle is 15 inches by 15 inches with an area of 225 in2. The length of the blue rectangle is marked -- it is 35 inches long. The width of the blue rectangle requires some calculation. Along the left side, the blue and orange is 30 inches long. But you can see from the right side of the orange that 15 inches of that is the orange. So the blue is also 15 inches (30 - 15). Thus, the area of the blue rectangle is  525 in2 (35 x 15). Altogether, the irregular shape is 750 in2 (225 + 525).

Any questions?

Jolene