Step by step
The question
Question: find the perimeter of this shape: a 20 by 8 rectangle with a semicircle on each end.
1 Find the edge
The perimeter is the way all around the edge.
There are two straight sides and two round ends.
Careful: the dashed line is inside the shape.
It is not on the edge, so we do not add it.
2 The two round ends
Each semicircle sits on an end of the rectangle.
So its diameter is 8.
The radius is half of it: 8 divided by 2 is 4.
The two round ends are two halves of a circle.
Together they are one whole circle: 2 times π times r.
2 times 4 is 8.
We write it as 8π.
3 Add all the sides
Walk around: the top, the bottom and the two round ends: 20 + 20 + 8π.
20 plus 20 is 40.
So the perimeter is 40 + 8π.
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.
8 times 3.14 is 25.12.
40 plus 25.12 is 65.12.
So the perimeter is about 65.12.
5 Check
Let's check it makes sense.
Each round end is 12.56.
It is longer than the straight line across it: 8.
It is shorter than going around the box corners: 4 + 8 + 4 = 16.
So the answer makes sense!
Let's look back.
First: find the edge.
Then: the two round ends.
Then: add all the sides.
Then: about how much.
Last: check.