Question

Find the area of the irregular figure 5 in. 6 in. 2 A = [? ]in. 7 in. 14 in. 14 in. 7 in 8 in

Answer 1

Given the irregular shape:

To determine the area of the shape, you have to divide it into smaller and simple figures, determine the area of each figure and then add them.

As you can see in the sketch above, I divided the irregular shape into three figures named A, B, and C. So, the first step is to determine the area of each shape:

Area of "A"

This shape is a rectangle with length l=8in and width w=7in. The area of A can be determined as the product of both dimensions:

`\begin{gathered} A_A=l_A\cdot w_A \\ A_A=8\cdot7 \\ A_A=56in^2 \end{gathered}`

Area of "B"

This shape is a rectangle with length l=22in and width w=7in, to determine the area you have to multiply both dimensions:

`\begin{gathered} A_B=l_B\cdot w_B \\ A_B=22\cdot7 \\ A_B=154in^2 \end{gathered}`

Area of "C"

Finally, C is a rectangle with length l=5in and width w=6in. You can determine its area as follows:

`\begin{gathered} A_C=l_C\cdot w_C \\ A_C=5\cdot6 \\ A_C=30in^2 \end{gathered}`

Once determined each area, you have to addd them to determine the area of the irregular shape:

`\begin{gathered} A_{\text{shape}}=A_A+A_B+A_C \\ A_{\text{shape}}=56+154+30 \\ A_{\text{shape}}=240in^2 \end{gathered}`