Step by step
The question
Question: find the area of this shape: a 12 by 4 rectangle with a semicircle on one end.
1 Split into parts
This shape is made of simple shapes.
A dashed line splits off the round end.
The rectangle is 12 by 4.
The round end is a semicircle: half of a circle.
2 Area of each part
The rectangle: length times width.
12 times 4 is 48.
The semicircle sits on the end of the rectangle.
So its diameter is 4.
The radius is half of it: 4 divided by 2 is 2.
The semicircle is half of a circle.
A circle is π times r squared.
So we take half.
2² means 2 times 2.
That is 4.
So it is half of π times 4.
Half of 4 is 2.
We write it as 2π.
3 Add the parts
The whole area is the two parts added: 48 + 2π.
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.
2 times 3.14 is 6.28.
48 plus 6.28 is 54.28.
So the area is about 54.28 square units.
5 Check
Let's check it makes sense.
The whole shape fits in a box 14 by 4: 56.
The area must be more than the rectangle alone: 48.
And less than the box: 56.
54.28 is between them.
So the answer makes sense!
Let's look back.
First: split into parts.
Then: area of each part.
Then: add the parts.
Then: about how much.
Last: check.