Step by step
The question
Question: find the height of a trapezoid with area 63 square units and parallel sides 5 and 13.
1 Use the rule
The height goes straight up from the base.
It makes a right angle with the base.
We know the area, so we start from the area rule.
Remember: two of them make a parallelogram.
The trapezoid is half of it.
So the area is half of (a + b) times h: A = ½ × (a + b) × h.
Now put the numbers in: A = 63, a = 5 and b = 13.
Brackets first: 5 plus 13 is 18.
Half of 18 means 18 divided by 2.
That is 9.
So 63 = 9 × h.
9 times h is written 9h.
Let's swap the two sides, so h is on the left.
2 Remove the 9
9h means 9 times h.
We want just h.
To remove times 9, we divide by 9.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
9 divided by 9 is 1.
So just h is left.
63 divided by 9 is 7.
So h = 7!
3 Check
Let's check: put h = 7 back in the area rule.
We get 63, the area in the question.
So the height is 7.
Let's look back.
First: use the rule.
Then: remove the 9.
Last: check.