Chapter 0.7, Problem 20E

To determine

To calculate: The perimeter of the figure provided below,

  

Answer to Problem 20E

The perimeter of the figure is $\text{14}\text{.3 m}$ .

Explanation of Solution

Given information:

The figure is provided below,

  

Formula used:

Circumference $\left(C\right)$ of a semi-circle with diameter d is given by $C=\frac{\pi d}{2}$ .

Perimeter $\left(P\right)$ of a figure is given by sum of all sides of the figure.

Calculation:

Consider the provided figure,

  

In the above figure the diameter of the semi-circle is 4m and the other two sides of the right angled triangle are 5m and 3m.

Here, the perimeter of figure is equal to the sum of circumference of semicircle and the two sides of the triangle.

Recall that the circumference $\left(C\right)$ of semi-circle with diameter d is given by $C=\frac{\pi d}{2}$ .

Apply it,

  $\begin{array}{c}C=\frac{3.14\times 4}{2}\\ =3.14\times 2\\ =\text{6}\text{.28 m}\end{array}$

Now, recall that the perimeter $\left(P\right)$ of a figure is given by sum of all sides of the figure.

Apply it,

  $\begin{array}{c}P=\text{6}\text{.28+5+3}\\ \text{=14}\text{.28 m}\end{array}$

Rounding off to the nearest tenth, we get,

  $P=14.3\text{ m}$

Thus, the perimeter of the figure is $\text{14}\text{.3 m}$ .