Question

What is the perimeter of a semicircle with a radius of 12?

Answer 1

perimeter = 61.7 units

Explanation:

The perimeter of a semicircle is equal to the sum of the length of the straight edge (diameter) and half the circumference of the circle.

To calculate the circumference of a circle, we have to use the following formula:

`{C = 2 \pi r}` ,

where C is the circumference and r is the radius of the circle.

Therefore, circumference of the full circle:

C = 2 × π × 12

= 24π

• As the semicircle has half the circumference of the full circle, its circumference is 24π ÷ 2 = 12π.

• We know that the diameter of a circle is twice its radius, and therefore the diameter of the semicircle = 12 × 2 = 24 units.

Now we have to simply add the circumference and diameter to get the perimeter of the semicircle:

perimeter = 12π + 24

= 61.7 units

Therefore the perimeter of the semicircle of radius 12 is 61.7 units.