Chapter 11.9, Problem 2CYU

To determine

To find the area of the composite figure.

Answer to Problem 2CYU

  $260.14$ square inches.

Explanation of Solution

Given information:Semicircle with diameter $d=22$ inches. Triangle with base $b=14$ inches and height $h=10$ inches.

Formula used: Area of semicircle $s=\frac{\pi \times r^2}{2}$ and area of triangle $a=\frac{1}{2}\times b\times h$ .

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

Calculation: Area of the semicircle $s=\frac{\pi \times r^2}{2}$

  $=\frac{\pi \times {11}^2}{2}$

On putting the value of radius.

  $=\frac{22\times 121}{7\times 2}$

On simplifying the expression.

  $=\frac{2662}{14}$

On converting the fraction.

  $=190.14$ square inches.

Area of the triangle $a=\frac{1}{2}\times b\times h$

  $=\frac{1}{2}\times 14\times 10$

On simplifying the expression.

  $=70$ square inches.

Adding $s+a$ would give the area of the composite figure.

  $=70+190.14$

This sums up to.

  $=260.14$ square inches.