Math CentralQuandaries & Queries


Question from Kassandra, a student:

I am trying to find out the perimeter of a semicircle. I do what the book says
but, I always get it wrong. I usually don't have problems with math until now.

There is half a circle. It shows that the radius of the circle is 4 units.

And then below the half circle there is a square below it. The angles are right angles
and the width is also 4 inches. I get close to the answer but, am usually off.

Please help.

Hi Kassandra,

Is this the diagram you are describing?

semicircle and square

The circumference (perimeter) of a circle is 2 π r where r is the radius of the circle and π is approximately 3.1416. Thus the circumference of half a circle is π r units which for your circle is 4 π units. The remaining perimeter of the figure is made up of 4 line segments, each of length 4 units. Thus the perimeter of this figure is

4 π + 4 × 4 units.

I hope this helps,

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