Question

A sign designer created a sign in the shape shown below.

The semicircles are congruent to one another with a diameter of 4 inches. What is the perimeter of the sign?
Answer







about 38 inches








about 78 inches








about 76 inches








about 80 inches

Answer 1

This is the sign:

Answer 2

The perimeter is the sum of the 4 sides. You know that two sides are 20 inches long, but the other two sides are a bit tricky since they are made up of 3 semicircles each.

Since the circumference (perimeter) of a circle is \[\Pi(d)\] Where d is the diameter.

Then half a circle's (semicircle) circumference (perimeter) must be \[1/2\Pi(d)\]

Letting \[\Pi=3.14\]
The perimeter of one of the semicircles must be \[1/2*3.14*4=6.28\] So the perimeter of three semicircles must be 3*6.28=18.84 inches

So now it's just the sum of all four sides.

18.84 inches + 20 inches + 18.84 inches + 20 inches = 77.68 inches