Step by step
The question
Question: find the area of a trapezoid with parallel sides 10 and 14 and height 6.
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: 14 + 10.
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 = 10, b = 14 and h = 6.
Brackets first: 10 plus 14 is 24.
Half of 24 means 24 divided by 2.
That is 12.
So A = 12 × 6.
12 times 6 is 72.
So the area is 72 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 14.
The top one has base 10.
Both have height 6.
Each is half of base times height.
We get 72 again.
So the area is right!
Let's look back.
First: two make a parallelogram.
Then: use the rule.
Last: check.