Step by step
The question
Question: find the area of a trapezoid with parallel sides 8 and 12 and height 5.
1 Two make a parallelogram
A trapezoid has one pair of parallel sides: the top and the bottom.
In some countries it is called a trapezium.
Take the same trapezoid again.
Turn it upside down and put it next to the first one.
Together they make a parallelogram.
Its base is the bottom of one and the top of the other: 12 + 8.
Our trapezoid is half of that parallelogram.
2 Use the rule
A parallelogram is base times height.
We take half: A = ½ × (a + b) × h.
Now put the numbers in: a = 8, b = 12 and h = 5.
Brackets first: 8 plus 12 is 20.
Half of 20 means 20 divided by 2.
That is 10.
So A = 10 × 5.
10 times 5 is 50.
So the area is 50 square units.
3 Check
Let's check another way.
A line from corner to corner cuts it into two triangles.
The bottom triangle has base 12.
The top one has base 8.
Both have height 5.
Each is half of base times height.
We get 50 again.
So the area is right!
Let's look back.
First: two make a parallelogram.
Then: use the rule.
Last: check.