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

Step-by-step 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 . However, since a semi circle is half a circle then the circumference is . Since the semi-circle adjoins the square, its diameter is the side length of the square 4cm.

So the total perimeter is