Worked examples
The question
Question: find the area of a parallelogram with base 10 and height 6.
1 Make a rectangle
A parallelogram has two pairs of parallel sides.
It looks like a rectangle pushed over.
The height goes straight up from the base.
It makes a right angle with the base.
Cut off the triangle at the left end.
Move it to the right end.
It fits exactly.
Now it is a rectangle, 10 long and 6 high.
Nothing was added or lost, so the area is the same.
2 Base times height
So the area is base times height: A = b × h.
A = b × h
Now put the numbers in: b = 10 and h = 6.
A = 10 × 6
10 times 6 is 60.
So the area is 60 square units.
A = 60
3 Check
Let's check another way.
A line from corner to corner cuts it into two triangles.
Each triangle is half of base times height.
Both have base 10 and height 6.
12 × 10 × 6 + 12 × 10 × 6 = 30 + 30 = 60
We get 60 again.
So the area is right!
Let's look back.
First: make a rectangle.
Then: base times height.
Last: check.
▶ Watch it solved
The question
Question: find the area of a parallelogram with base 10 cm and height 6 cm.
The slanted side is 7 cm.
1 Make a rectangle
A parallelogram has two pairs of parallel sides.
It looks like a rectangle pushed over.
The height goes straight up from the base.
It makes a right angle with the base.
Cut off the triangle at the left end.
Move it to the right end.
It fits exactly.
Now it is a rectangle, 10 cm long and 6 cm high.
Nothing was added or lost, so the area is the same.
Careful: the slanted side is 7 cm.
It is not the height.
The height goes straight up.
2 Base times height
So the area is base times height: A = b × h.
A = b × h
Now put the numbers in: b = 10 and h = 6.
A = 10 × 6
10 times 6 is 60.
So the area is 60 cm².
A = 60 cm2
3 Check
Let's check another way.
A line from corner to corner cuts it into two triangles.
Each triangle is half of base times height.
Both have base 10 and height 6.
12 × 10 × 6 + 12 × 10 × 6 = 30 + 30 = 60
We get 60 again.
So the area is right!
Let's look back.
First: make a rectangle.
Then: base times height.
Last: check.
▶ Watch it solved
The question
Question: find the height of a parallelogram with area 48 square units and base 8.
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: move the end triangle and it is a rectangle.
So the area is base times height: A = b × h.
A = b × h
Now put the numbers in: A = 48 and b = 8.
48 = 8 × h
8 times h is written 8h.
Let's swap the two sides, so h is on the left.
8h = 48
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.
8h8 = 488
8 divided by 8 is 1.
So just h is left.
48 divided by 8 is 6.
488 = 6
So h = 6!
h = 6
3 Check
Let's check: put h = 6 back in the area rule.
b × h = 8 × 6 = 48
We get 48, the area in the question.
So the height is 6.
Let's look back.
First: use the rule.
Then: remove the 8.
Last: check.
▶ Watch it solved
