Chapter 11.6, Problem 19WE

To determine

To Find: The area inside the circle and outside the rectangle.

Answer to Problem 19WE

  $A=100\pi -192sq.units$

Explanation of Solution

Given: A rectangle with length $16cm$ and width $12cm$ inscribed in a circle.

  

Using Pythagoras theorem

  $\begin{array}{l}{d}^2={16}^2+{12}^2\\ d^2=256+144\\ d^2=400\\ d=20\end{array}$

Area of shaded region.

  $\begin{array}{l}A=\frac{\pi d^2}{4}-lb\\ A=\frac{\pi {(20)}^2}{4}-(16)(12)\\ A=\frac{400\pi }{4}-192\\ A=100\pi -192sq.units\end{array}$

Hence, $A=100\pi -192sq.units$