Chapter 16.2, Problem 2PS

To determine

To find: Thearea of the circle in the given diagram.

Answer to Problem 2PS

The area of the circle in the given diagram is $157.079{\text{unit}}^2$ .

Explanation of Solution

Given information:

The given figure is,

  

Calculate the diameter of the circle as,

  $\begin{array}{c}D=\frac{10}{\sin 45°}\\ =10\sqrt{2}\text{unit}\end{array}$

The area of the circle is calculated as,

  $\begin{array}{c}A=\frac{\pi }{4}{D}^2\\ =\frac{\pi }{4}{\left(10\sqrt{2}\right)}^2\\ =157.079{\text{unit}}^2\end{array}$

Thus, the area of the circle in the given diagram is $157.079{\text{unit}}^2$ .