Chapter 11.9, Problem 14PPS

To determine

To calculate the area of the figure.

Answer to Problem 14PPS

  $89.3$ square feet.

Explanation of Solution

Given information:

The figure consists of a rectangle and a semicircle.

Rectangle has a length of $l=10$ feet and breadth $b=7$ feet.

Semicircle has a diameter $d=7$ , hence radius $r=\frac{d}{2}$

  $=\frac{7}{2}$ feet.

Formula used: Area of rectangle $a=l\times b$ where ‘l’ is the length and ‘b’ is the breadth.

Area of semicircle $s=\frac{\pi \times r^2}{2}$ where ‘r’ is the radius.

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

Calculation:

Area of the rectangle

  $a=l\times b$

Putting values in the same

  $=10\times 7$

Multiply the expression

  $=70$ square feet

Area of semicircle

  $s=\frac{\pi \times r^2}{2}$

Formula for area of semicircle.

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

Putting the values in the formula

  $=\frac{11\times 7}{4}$

Dividing common terms and simplifying

  $=19.25$ square feet.

Now, add the two areas to get the area of the given figure.

  $=a+s$

  $=70+19.25$

It becomes

  $=89.25$

After rounding this to the nearest tenth

  $=89.3$ square feet,