Question

A parallelogram has an area of 96 cm2 and a height of 4 cm. What is the base length of the parallelogram? Explain your steps to solving the problem.

Answer 1

Do you know how to find the area of a parallelogram?

Answer 2

Here is parallelogram ABCD.

area of a parallelogram = base * height

Answer 3

A = bh

You know A and h. Plug in the numbers and solve for b.

Answer 4

Not being stupid but this is a little confusing.

Answer 5

Ok, let's go over it, one step at a time.

The formula for the area of a parallelogram is A = bh, where A = area, b = base, and h = height.

Ok so far?

Answer 6

Yeah

Answer 7

That means if I asked you to find the area of a parallelogram with a base of 5 cm and a height of 2 cm, you'd do

A = bh
A = 5 cm * 2 cm
A = 10 cm^2

Ok?

Answer 8

Yeah so it's basically multiplication then?

Answer 9

Right.
Now what if I asked you a question based on the area of a parallelogram, but with a little twist.

Here's the question.
A parallelogram has an area of 10 cm^2 and a height of 2 cm. What is the base?

Answer 10

We know the formula for the area of a parallelogram is

A = bh

We know b = 10 cm^2 and h = 2 cm
We are looking for b.

Answer 11

Is it 12 cm 2?

Answer 12

First, we write the formula

A = bh

Now we replace the variables with the numbers we are given.
Since A = 10 cm^2 and h = 2 cm, we replace A and h with those numbers in the formula.

10 cm^2 = b * 2 cm

Now we divide both sides by 2 cm:

(10 cm^2)/(2 cm) = b

b = 5 cm

Answer 13

Since the base times the height equals the area, the base equals the area divided by the height.

Answer 14

Oh, now I get it.

Answer 15

Great.

Now let's go back to your original problem.

The area is 96 cm^2.
The height is 4 cm.
Since the base times the height equals the area, that means the area divided by the height equals the base.

We divide 96 cm^2 by 4 cm to find the base.

Answer 16

So is the answer 24 cm2??

Answer 17

Am I right with the answer?

Answer 18

thanks for all your help mathstudent55 :)

Answer 19

Yes, the answer is 24 cm.

Now to check, all you need to do is find the area of a parallelogram with base 24 cm and height 4 cm. We must get an area of 96 cm^2.

A = bh
A = 24 cm * 4 cm
A = 96 cm^2

Since you end up with the area the problem told you, this confirms the base is 24 cm.