Chapter A.2, Problem 39AYU

To determine

Find the area of shaded region.

Answer to Problem 39AYU

  $\boxed{A=2\pi unit{s}^2}$

Explanation of Solution

Given information:

Find the area of shaded region.

  

Calculation:

Consider the sheded region which is area of circleThe diameter of circle is equivalent to diagonal length of the square.

The diagonal divide the square in to two right triangles and diagonal acts as a hypotaneus.

  $\begin{array}{l}{d}^2=2^2+2^2\\ =4+4\\ =8\\ d=2\sqrt{2}\end{array}$

  $\begin{array}{l}Diameter=2\sqrt{2}unit\\ radius=2\sqrt{2}/2=\sqrt{2}unit\end{array}$

Now find the area of the circle.

  $A=\pi r^2$

Substitute the given values in above expression, we get

  $\begin{array}{l}A=\pi \times {\left(\sqrt{2}\right)}^2\\ A=\pi \times 2\\ A=2\pi unit{s}^2\end{array}$

  $\boxed{A=2\pi unit{s}^2}$

Hence, area of shaded regionis $\boxed{A=2\pi unit{s}^2}$ .