Question

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

What is the exact perimeter of the figure?


4π+16 cm

4π+12 cm

2π+6 cm

2π+12 cm
Square with 2 sides labeled 4cm. A semicircle adjoins the left side of the square. Inside lines are dashed

Answer 1

Answer: 4pi + 12

Explanation:

TEST :)

Answer 2

`4\pi + 12`

Explanation:

The perimeter of a square is P = 4s where s is the side length. The perimeter of the square is P = 4*4 = 16 cm. However, one side is covered by a semi circle and its length of 4 cm is not a part of the perimeter. So it is 16 - 4 = 12. The perimeter of the square s 12.

To find the perimeter of a semi-circle use the circumference formula. The circumference is
`C = 2\pi d`. However, since a semi circle is half a circle then the circumference is
`C = \pi d`. Since the semi-circle adjoins the square, its diameter is the side length of the square 4cm.

`C = \pi * 4 \\C= 4\pi`

So the total perimeter is
`4\pi + 12`