Step by step
The question
Question: find the area of a trapezoid with parallel sides 7.5 cm and 12 cm and height 6 cm.
1 Two make a parallelogram
A trapezoid has one pair of parallel sides: the top and the bottom.
Parallel means they never meet, like train tracks.
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 bottom is the bottom of one and the top of the other, end to end: 12 + 7.5.
The two copies are the same.
So our trapezoid is exactly half of that parallelogram.
2 Use the rule
a and b are the two parallel sides.
The big parallelogram is base times height: (a + b) × h.
Our trapezoid is half of it: A = ½ × (a + b) × h.
Now put the numbers in: a = 7.5, b = 12 and h = 6.
Brackets first: 7.5 plus 12 is 19.5.
Half of 19.5 is not a whole number.
Times can be done in any order, so we take half of 6 instead: 6 divided by 2 is 3.
So A = 19.5 × 3.
Forget the points: 195 times 3 is 585.
19.5 is 195 tenths.
So the answer is 585 tenths.
That is 1 digit after the point: 58.5.
So the area is 58.5 cm².
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 7.5.
Both have height 6.
Each is half of base times height.
We get 58.5 again.
So the area is right!
Let's look back.
First: two make a parallelogram.
Then: use the rule.
Last: check.