Question

The figure is made up of two shapes, a semicircle and a rectangle.

What is the exact perimeter of the figure?

A. 4 pi + 26 in.

B. 8 pi + 34 in.

C. 4 pi + 34 in.

D. 8 pi + 72 in.

Answer 1

perimeter of quadrilateral +perimeter of curved shape=26+4pi

Answer 2

Option A
`(4 \pi+26)\ in`

Explanation:

we know that

The perimeter of the figure is equivalent to the perimeter of a rectangle plus the perimeter of semicircle minus the length side of
`8` inches

step 1

Find the perimeter of rectangle

the perimeter of rectangle is equal to

`P=2(b+h)`

we have

`b=8\ in`

`h=9\ in`

substitute

`P=2(8+9)=34\ in`

step 2

Find the circumference of semicircle

the of circumference of semicircle is equal to

`C=(1)/(2)\pi D`

we have

`D=8\ in`

substitute

`C=(1)/(2)\pi (8)=4 \pi\ in`

step 3

Find the perimeter of the figure

`34\ in+4 \pi\ in-8\ in=(4 \pi+26)\ in`