Chapter 11.9, Problem 19PPS

To determine

To calculate the area of the shaded region.

Answer to Problem 19PPS

  $40.9$ square meters.

Explanation of Solution

Given information:

The figure consists of a square and a circle.

Square has a side $a=8.5$ meters.

Circle has a radius $r=6$ meters.

Formula used: Area of square $s=a^2$ where ‘a’ is the side of the square.

Area of circle $c=\pi \times r^2$ where ‘r’ is the radius.

For calculations, $\pi =\frac{22}{7}$ has been used.

Calculation:

To calculate area of the shaded region, subtract the area of the square from the area of the circle.

  $s=a^2$

Area of the square.

  $=a\times a$

Expanding the portion of ‘a’.

  $=8.5\times 8.5$

Multiplying the same.

  $=72.25$ square meters.

Calculation of the area of the circle

  $c=\pi \times r^2$

Formula of area of circle

  $=\frac{22}{7}\times 6^2$

Putting the value of radius in the formula.

  $=\frac{22\times 36}{7}$

Simplifying of the same.

  $=113.14$ square meters.

Now, area of the shaded region

  $=c-s$

Subtract the area of the square from area of circle.

  $=113.14-72.25$

Numeric values of the respective shapes.

  $=40.89$

Rounding off to the nearest tenth.

  $=40.9$ square meters.