Chapter 4.6, Problem 57E

To determine

To find:The area of the shaded region in square inches.

Answer to Problem 57E

The area of shaded region is $24$ .

Explanation of Solution

Given information:

The diagram is,

  

Area of shaded region is given by subtracting the area of small triangle from the area of large triangle.

The formula for calculating area of triangle is $\frac{1}{2}b\times h$ .

  $\begin{array}{c}\text{area}\text{of}\text{large}\text{triangle}=\frac{1}{2}\times 9\times 7\\ =31.5\end{array}$

  $\begin{array}{c}\text{area}\text{of}\text{large}\text{triangle}=\frac{1}{2}\times 5\times 3\\ =7.5\end{array}$

Now, area of shaded region is given as,

  $\begin{array}{c}\text{Area }\text{of}\text{shaded}\text{region}=\left(\text{Area}\text{of}\text{large}\text{triangle}\right)-\left(\text{Area}\text{of}\text{small}\text{triangle}\right)\\ \text{=31}\text{.5}-\text{7}\text{.5}\\ \text{=24}\end{array}$

Therefore, the area of shaded region is $24$ .