Chapter 11.4, Problem 4BCYP

To determine

To find: the area of given figure and round to the nearest tenth if necessary.

Answer to Problem 4BCYP

Therefore the Area of the figure is 374.5 cm.

Explanation of Solution

Given information: The given figure is:

  

Calculation:

The given figure can be shown as below.

  

The area of the figure can be separated into a right triangle with a hypotenuse of 15 cm, and a leg measuring 31-22=9 cm, and height is $\sqrt{{15}^2-9^2}=12$ (By Pythagorean Theorem),and a rectangle with a length of 22 cm and width of 12 (height of the triangle) and a semi-circle of diameter 12 (height of the triangle) or radius 6.

Area of the figure=Area of the triangle + Area of the rectangle + Area of the semicircle

  $\begin{array}{l}=\frac{1}{2}.b.h+l.w+\frac{1}{2}.\pi r^2.\\ =\frac{1}{2}\times 9\times 12+22\times 12+\frac{1}{2}\times 3.14\times 6^2.\\ =54+264+56.52\\ =374.52cm\\ \approx 374.5cm(\text{Round}\text{to}\text{tenth}).\end{array}$

Therefore the Area of the figure is 374.5 cm.