Step by step
The question
Question: find the perimeter of this shape: a 10 by 6 rectangle with a semicircle on the long side.
1 Find the edge
The perimeter is the way all around the edge.
There are three straight sides
and one round top.
The dashed line is inside the shape.
It is not on the edge.
2 The round top
The semicircle sits on the long side of the rectangle.
So its diameter is 10.
The radius is half of it: 10 divided by 2 is 5.
Careful!
The semicircle sits on the long side, 10.
Its radius is half of 10, not half of 6.
The round top 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 5.
We write it as 5π.
3 Add all the sides
Walk around: the bottom, the two sides, then the curve: 10 + 6 + 6 + 5π.
10 plus 6 plus 6 is 22.
So the perimeter is 22 + 5π.
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.
5 times 3.14 is 15.7.
22 plus 15.7 is 37.7.
So the perimeter is about 37.7.
5 Check
Let's check it makes sense.
The round top is about 15.7.
It is longer than the straight line under it: 10.
It is shorter than going around the box corners: 5 + 10 + 5 = 20.
So the answer makes sense!
Let's look back.
First: find the edge.
Then: the round top.
Then: add all the sides.
Then: about how much.
Last: check.