Step by step
The question
Question: find the area of this shape: a 10 by 6 rectangle with a semicircle on the long side.
1 Split into parts
This shape is made of simple shapes.
A dashed line splits off the round top.
The rectangle is 10 by 6.
The round top is a semicircle: half of a circle.
2 Area of each part
The rectangle: length times width.
10 times 6 is 60.
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 semicircle is half of a circle.
A circle is π times r squared.
So we take half.
5² means 5 times 5.
That is 25.
So it is half of π times 25.
Half of 25 is 12.5.
We write it as 12.5π.
3 Add the parts
The whole area is the two parts added: 60 + 12.5π.
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.
Forget the points: 125 times 314 is 39250.
Together, the numbers have 1 + 2 = 3 digits after the point.
So the answer has 3 too: 39.250, which is 39.25.
So we have 60 + 39.25.
60 plus 39.25 is 99.25.
So the area is about 99.25 square units.
5 Check
Let's check it makes sense.
The whole shape fits in a box 10 by 11: 110.
Let's check it makes sense.
The area must be more than the rectangle alone: 60.
And less than the box: 110.
99.25 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.