Chapter 11.9, Problem 10PPS

To determine

To calculate the area of the figure.

Answer to Problem 10PPS

  $232.9$ square inches.

Explanation of Solution

Given information:

The figure is can be divided into a trapezoid and a semicircle.

Trapezoid has parallel side of $a=9$ inches and $b=18$ inches and height $h=9$ inches.

Semicircle has a diameter $d=9$ , hence radius $r=\frac{d}{2}$

  $=\frac{9}{2}$

  $=4.5$ inches.

Formula used: Area of trapezoid $t=\frac{a+b}{2}\times h$ where ‘a’ and ‘b’ are parallel sides while ‘h’ is the height.

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 trapezoid

  $t=\frac{a+b}{2}\times h$

Formula of area of trapezoid

  $=\frac{9+18}{2}\times 9$

Simplify the expression

  $=\frac{27\times 9}{2}$

Further simplification

  $=\frac{243}{2}$

  $=121.5$ square inches

Area of semicircle

  $s=\frac{\pi \times r^2}{2}$

Formula for area of semicircle.

  $=\frac{22}{7\times 2}\times {4.5}^2$

Putting the values in the formula

  $=\frac{11}{2}\times 20.25$

Simplify the expression

  $=111.38$ square inches.

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

  $=t+s$

  $=121.5+111.38$

It becomes

  $=232.88$

After rounding this to the nearest tenth

  $=232.9$ square inches,