Chapter 11.5, Problem 15WE

To determine

To Find: The area of the mat that is not used for wrestling.

Answer to Problem 15WE

  $984f{t}^2$

Explanation of Solution

Given: A school wrestling mat is a square with $40ft$ sides. A circle $28ft$ in diameter is painted on mat. No wrestling is allowed outside the circle.

  

Radius of circle

  $r=\frac{d}{2}=\frac{28}{2}=14$

Area of shaded part is not used for wrestling.

Area of shaded part = Area of square − area of circle

  $\begin{array}{l}A=A_s-A_c\\ $ A={(side)}^2-\pi r^2$$ A={(40)}^2-\left(\frac{22}{7}{(14)}^2\right)$A=1600-616\\ A=984f{t}^2\end{array}$

Hence, area not used for wrestling is $984f{t}^2$ .