Chapter 11.4, Problem 6CYU

To determine

To find: The area of each figure.

Answer to Problem 6CYU

The area of figure is $71.6{\text{in}}^2$ .

Explanation of Solution

Given:

The given figure is:

  

Calculation:

To find the area of the figure, subtract the area of the triangle from the area of rectangle.

Use Pythagorean Theorem, the height $h$ of the triangle is calculated as:

  $\begin{array}{c}h=\sqrt{{4.5}^2-4^2}\\ =\sqrt{20.25-16}\\ =\sqrt{4.25}\\ =2.1\end{array}$

Height of the triangle is $2.1\text{meters}$ .

Area of isosceles triangle with base $4\text{in}$ is calculated as:

  $\begin{array}{c}\text{Area}=\frac{1}{2}\text{×base×height}\\ =\frac{1}{2}\text{×8×2}\text{.1}\\ =8.4\end{array}$

Area of shaded region is calculated as:

  $\begin{array}{c}\text{Area of figure}=\text{Area of rectangle}-\text{Area of triangle}\\ =\text{length×breadth}-\frac{1}{2}\text{×base×height}\\ =10\times 8-8.4\\ =71.6\end{array}$ .

Therefore the area of figure is $71.6{\text{in}}^2$ .