Step by step
The question
Question: find the area of a trapezoid with parallel sides 6 cm and 10 cm and height 4 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: 10 + 6.
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 = 6, b = 10 and h = 4.
Brackets first: 6 plus 10 is 16.
Half of 16 means 16 divided by 2.
That is 8.
So A = 8 × 4.
8 times 4 is 32.
So the area is 32 cm².
3 Check
Let's check another way.
A line from corner to corner cuts it into two triangles.
The bottom triangle has base 10.
The top one has base 6.
Both have height 4.
Each is half of base times height.
We get 32 again.
So the area is right!
Let's look back.
First: two make a parallelogram.
Then: use the rule.
Last: check.