Question

The figure is made up of two shapes, a semicircle and a square. What is the exact perimeter of the figure?

A) 4 π + 16 cm
B) 2 π + 6 cm
C) 4 π + 12 cm
D) 2 π + 12 cm
Please help

Answer 1

3 sides X 4 cm = 12 cm. So answer must be one of last two.

perimeter of circle = pi X diameter
this is a 1/2 circle, so 1/2 of diameter = radius.
1/2 of 4 (diameter) = 2

so 2 pi + 12 is answer

Answer 2

Option
`(2 \pi+12)\ cm`

Explanation:

we know that

The perimeter of the figure is equal to sum the length of semicircle plus the length of three sides of a square

Find the length of semicircle

Remember that the circumference of semicircle is equal to

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

we have

`D=4\ cm`

substitute

`C=(1)/(2)\pi(4)=2 \pi\ cm`

The perimeter of the figure is equal to

`P=2 \pi+3(4)=(2 \pi+12)\ cm`