Step by step
The question
Question: find the area of this shape: an 8 by 4 rectangle with a triangle on top, 3 high, and a semicircle on the end.
1 Split into parts
This shape is made of three simple shapes.
Dashed lines split them.
The rectangle is 8 by 4.
The triangle sits on top.
Its base is 8, its height 3.
The round end is a semicircle: half of a circle.
2 Area of each part
The rectangle: length times width.
8 times 4 is 32.
The triangle: half of base times height.
8 times 3 is 24.
Half of 24 means 24 divided by 2.
That is 12.
So the triangle is 12 square units.
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 three parts added: 32 + 12 + 2π.
32 plus 12 is 44.
So the area is 44 + 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.
44 plus 6.28 is 50.28.
So the area is about 50.28 square units.
5 Check
Let's check it makes sense.
The whole shape fits in a box 10 by 7: 70.
Let's check it makes sense.
The area must be more than the rectangle and the triangle: 44.
And less than the box: 70.
50.28 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.