Question

Find the perimeter of this figure to the nearest hundredth. Use 3.14 to approximate π P=_ ft

Answer 1

Given:

The dimensions of the rectangle are 8 ft and 10 ft.

The diameter of the semicircle is 8 ft.

The objective is to find the perimeter of the figure.

By considering the figure, the formula to find the perimeter is,

`\begin{gathered} P=P\text{ of rectangle+P of hemisphere} \\ =\lbrack2(l+b)\rbrack+\lbrack\pi r+D\rbrack \end{gathered}`

The radius of the hemisphere can be calculated as,

`\begin{gathered} r=(D)/(2) \\ =(8)/(2) \\ =4\text{ ft} \end{gathered}`

Now, substitute the given values in the above formula.

`\begin{gathered} P=\lbrack2(10+8)\rbrack+\lbrack3.14\cdot4+8\rbrack \\ =\lbrack2(18)\rbrack+\lbrack12.56+8\rbrack \\ =36+20.56 \\ =56.56 \end{gathered}`

Hence, the perimeter of the figure is 56.56 ft.