Question

The figures below are based on semicircles and squares. Find the perimeter and the area of each shape. Give your answer as a completely simplified exact value in terms of π (no approximations).

Answer 1

Answer:

Part 1) The area of the figure is $A=48\ cm^2$

Part 2) The perimeter of the figure is $P=4(2+3\pi)\ cm$

Step-by-step explanation:

Part 1) Find the area of the figure

we know that

The area of the figure is equal to the area of three squares

so

$A=3[4^2]=48\ cm^2$

Part 2) Find the perimeter of the figure

we know that

The perimeter of the figure is equal to two times the length side of the square, plus the circumference of six semicircles ( or the circumference of three circles)

Remember that

The circumference of a circle is equal to

$C=\pi D$

where

D is the diameter of the circle

In this problem

$D=4\ cm$

so

$P=2(4)+3[\pi(4)]=(8+12\pi)\ cm$

simplify

$P=4(2+3\pi)\ cm$