Step by step
The question
Question: find the perimeter of this shape: a 12 cm by 4 cm 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 4 cm.
The radius is half of it: 4 divided by 2 is 2.
The two round ends are two halves of a circle.
Together they are one whole circle: 2 times π times r.
2 times 2 is 4.
We write it as 4π.
3 Add all the sides
Walk around: the top, the bottom and the two round ends: 12 + 12 + 4π.
12 plus 12 is 24.
So the perimeter is 24 + 4π.
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.
4 times 3.14 is 12.56.
24 plus 12.56 is 36.56.
So the perimeter is about 36.56 cm.
5 Check
Let's check it makes sense.
Each round end is 6.28.
It is longer than the straight line across it: 4.
It is shorter than going around the box corners: 2 + 4 + 2 = 8.
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.