Perimeter of square 6 with a semicircle on the end

Step by step

The question

Question: find the perimeter of this shape: a 6 square with a semicircle on one end.

1 Find the edge

The perimeter is the way all around the edge.

There are three straight sides and one round end.

Careful: the dashed line is inside the shape.

It is not on the edge, so we do not add it.

2 The round end

The semicircle sits on the end of the square.

So its diameter is 6.

The radius is half of it: 6 divided by 2 is 3.

The round end is half of a circle.

The way round a circle is 2 times π times r.

We take half.

Half of 2 is 1.

So it is just π times 3.

We write it as 3π.

3 Add all the sides

Walk around: the top, the left side, the bottom, then the curve: 6 + 6 + 6 + 3π.

6 plus 6 plus 6 is 18.

So the perimeter is 18 + 3π.

We keep π in the answer.

That is the exact answer.

4 About how much

To see about how much, put 3.14 for π.

3 times 3.14 is 9.42.

18 plus 9.42 is 27.42.

So the perimeter is about 27.42.

5 Check

Let's check it makes sense.

The round end is 9.42.

It is longer than the straight line across it: 6.

It is shorter than going around the box corners: 3 + 6 + 3 = 12.

So the answer makes sense!

Let's look back.

First: find the edge.

Then: the round end.

Then: add all the sides.

Then: about how much.

Last: check.