Step by step
The question
Question: find the area of this shape: an 8 m by 5 m rectangle with a triangle on top, 2 m high.
1 Split into parts
This shape is made of simple shapes.
A dashed line splits it into a rectangle and a triangle.
The rectangle is 8 by 5.
The triangle sits on top.
Its base is the top of the rectangle: 8 m.
Its height is 2 m.
2 Area of each part
The rectangle: length times width.
8 times 5 is 40.
The triangle: half of base times height.
8 times 2 is 16.
Half of 16 means 16 divided by 2.
That is 8.
So the triangle is 8 m².
3 Add the parts
The whole area is the two parts added.
40 plus 8 is 48.
So the area is 48 m².
4 Check
Let's check another way.
Draw a box around the whole shape: 8 by 7.
Take away the two empty corners.
Each is half of a 4 by 2 box.
So together they are 4 × 2.
We get 48 again.
So the area is right!
Let's look back.
First: split into parts.
Then: area of each part.
Then: add the parts.
Last: check.