Step by step
The question
Question: find the height of a trapezoid with area 40 square units and parallel sides 6 and 10.
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 = 40, a = 6 and b = 10.
Brackets first: 6 plus 10 is 16.
Half of 16 means 16 divided by 2.
That is 8.
So 40 = 8 × h.
8 times h is written 8h.
Let's swap the two sides, so h is on the left.
2 Remove the 8
8h means 8 times h.
We want just h.
To remove times 8, we divide by 8.
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.
8 divided by 8 is 1.
So just h is left.
40 divided by 8 is 5.
So h = 5!
3 Check
Let's check: put h = 5 back in the area rule.
We get 40, the area in the question.
So the height is 5.
Let's look back.
First: use the rule.
Then: remove the 8.
Last: check.