Chapter 11.9, Problem 21PPS

To determine

To calculate the area of the shaded region.

Answer to Problem 21PPS

  $30.2$ square inches.

Explanation of Solution

Given information:

The figure consists of a rectangle and a semicircle.

Rectangle has length $l=8$ inches and breadth $b=5$ .

Semicircle has diameter $d=5$ . Radius $r=\frac{d}{2}$

  $=\frac{5}{2}$ .

Formula used: Area of rectangle $a=l\times b$ .

Area of semicircle $s=\frac{\pi \times r^2}{2}$ .

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

Calculation:

To calculate area of the shaded region, subtract the area of the semicircle from the area of the rectangle.

  $a=l\times b$

Area of the rectangle’s formula.

  $=8\times 5$

Applying values in the formula.

  $=40$ square inches.

Area of the unshaded semi-circle.

  $s=\frac{\pi \times r^2}{2}$

Formula for area of semicircle.

  $=\frac{22}{7\times 2}\times \frac{5}{2}\times \frac{5}{2}$

Putting the values in the formula.

  $=\frac{11\times 25}{7\times 4}$

Simplifying the same.

  $=9.82$ square inches.

Now, area of the shaded region

  $=a-s$

Subtract the area of the semicircle from area of rectangle.

  $=40-9.82$

Numeric values of the respective shapes.

  $=30.18$

Rounding off to the nearest tenth.

  $=30.2$ square inches.