Question

Find the perimeter and the area of the composite figure

a. What is the approximate perimeter of the concrete region? Use 3.14 for π

b. What is the exact area of the concrete region? Leave answers in terms of π.

Answer 1

Part A) The approximate perimeter of the concrete region is
`P=64.66\ yd`

Par B) The exact area of the concrete region is
`A=(8\pi+162.4)\ yd^(2)`

Explanation:

Part A) What is the approximate perimeter of the concrete region?

we know that

The perimeter of the composite figure is equal to

`P=\pi r+2(15.2)+ 11.5+10.2`

The radius of semicircle is

`r=8/2=4\ yd`

substitute

`P=(3.14)(4)+2(15.2)+ 11.5+10.2=64.66\ yd`

Part B) What is the exact area of the concrete region?

we know that

The area of the composite figure is equal to the area of semicircle plus the area of rectangle plus the area of triangle

so

`A=(1)/(2) \pi r^(2) +(15.2)(8)+(1)/(2)(10.2)(8)`

The radius of semicircle is

`r=8/2=4\ yd`

`A=(1)/(2) \pi (4)^(2) +(15.2)(8)+(1)/(2)(10.2)(8)`

`A=8\pi+121.6+40.8`

`A=(8\pi+162.4)\ yd^(2)`