Area of parallelogram base 9, side 6, height 5

Step by step

The question

Question: find the area of a parallelogram with base 9 and height 5.

The slanted side is 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, 9 long and 5 high.

Nothing was added or lost, so the area is the same.

Careful: the slanted side is 6.

It is not the height.

The height goes straight up.

2 Base times height

So the area is base times height: A = b × h.

Now put the numbers in: b = 9 and h = 5.

9 times 5 is 45.

So the area is 45 square units.

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 9 and height 5.

We get 45 again.

So the area is right!

Let's look back.

First: make a rectangle.

Then: base times height.

Last: check.