Chapter 11, Problem 2E

To determine

To calculate the area of the shaded region.

Answer to Problem 2E

  $7.74$ square feet.

Explanation of Solution

Given information:

The figure consists of a square and a circle.

Square has a side $a=6$ feet.

Circle has a diameter $d=6$ feet. Hence radius $r=\frac{d}{2}$

  $=\frac{6}{2}$

  $=3$ feet.

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, $\pi =3.14$ 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’.

  $=6\times 6$

Multiplying the same.

  $=36$ square feet.

Calculation of the area of the circle

  $c=\pi \times r^2$

Formula of area of circle

  $=3.14\times 3^2$

Putting the value of radius in the formula.

  $=3.14\times 9$

Simplifying of the same.

  $=28.26$ square feet.

Now, area of the shaded region

  $=c-s$

Subtract the area of the square from area of circle.

  $=36-28.26$

Numeric values of the respective shapes.

  $=7.74$ square feet, rounding off to the nearest hundredth.