Chapter 11.9, Problem 15PPS

a.

To determine

To calculate the area of the figure.

Answer to Problem 15PPS

  $73.1$ square inches.

Explanation of Solution

Given information:

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

Formula used:

Area of triangle $a=\frac{1}{2}\times b\times h$ where breadth $b=8$ inches and height $h=12$ inches.

Area of semicircle $s=\frac{\pi \times r^2}{2}$ where diameter is the same as the base of the triangle mention above. Hence diameter $d=b=8$ , so the radius $r=\frac{d}{2}$

  $=\frac{8}{2}=4$ inches.

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

Calculation:

Area of the triangle

  $a=\frac{1}{2}\times b\times h$

Formula of area of triangle

  $=\frac{1}{2}\times 8\times 12$

Simplify the expression

  $=4\times 12$

On multiplying

  $=48$ square inches

Area of the semicircle

  $s=\frac{\pi \times r^2}{2}$

Formula of area of semicircle

  $=\frac{22\times 4^2}{7\times 2}$

Simplify the expression

  $=\frac{11\times 16}{7}$

This leads to

  $=25.14$ square inches

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

  $=a+s$

  $=48+25.14$

Hence the sum of areas

  $=73.14$

Rounding to the nearest tenth.

  $=73.1$ square inches.

b.

To determine

To calculate the area of the figure.

Answer to Problem 15PPS

  $104.6$ square inches.

Explanation of Solution

Given information:

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

Formula used:

Area of triangle $a=\frac{1}{2}\times b\times h$ where breadth $b=8$ inches and height $h=12$ inches.

Area of semicircle $s=\frac{\pi \times r^2}{2}$ where diameter is the same as the base of the triangle mention above. Hence diameter $d=h=12$ , so the radius $r=\frac{d}{2}$

  $=\frac{12}{2}=6$ inches.

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

Calculation:

Area of the triangle

  $a=\frac{1}{2}\times b\times h$

Formula of area of triangle.

  $=\frac{1}{2}\times 8\times 12$

Simplify the expression

  $=4\times 12$

On multiplying

  $=48$ square inches

Area of the semicircle

  $s=\frac{\pi \times r^2}{2}$

Formula of area of semicircle

  $=\frac{22\times 6^2}{7\times 2}$

Simplify the expression

  $=\frac{11\times 36}{7}$

This leads to

  $=56.57$ square inches

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

  $=a+s$

  $=48+56.57$

Hence the sum of areas

  $=104.57$

Rounding to the nearest tenth.

  $=104.6$ square inches.