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# Unknown Dimensions of Parallelograms

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Have you ever watched someone else work on a project?

Jillian loves watching the other women work on their quilt squares. One of the ladies, Marie, came with her quilt pattern already cut out. The quilt square was designed to be filled with parallelograms and triangles.

"How much material are you using for one parallelogram?" Jillian asked her.

"I am using 18 square inches of material," Marie told Jillian.

Jillian watched her measure the length of the base of the parallelogram and noticed that it was 6 inches long.

"Hmmm," thought Jillian. "Now I can figure out the height of the parallelogram."

Can you use this given information to figure out the height?

This Concept is all about finding unknown dimensions of parallelograms. Pay close attention and you will know how to do this at the end of the Concept.

### Guidance

We can also work to figure out a missing dimension if we have been given the area and another measurement.

We can be given the area and the height or the area and the base.

This is a bit like being a detective. You will need to work backwards to figure out the missing dimension.

Let’s look at figuring out the base first.

A parallelogram has an area of 48 square inches and a height of 6 inches. What is the measurement of the base?

To figure this out, let’s look at what we know to do. The area of a parallelogram is found by multiplying the base and the height. If we are looking for the base or the height, we can work backwards by dividing.

We divide the given area by the given height or given base.

48 $\div$ 6 $=$ 8

The measurement of the base is 8 inches.

This will work the same way if we are looking for the height.

A parallelogram has an area of 54 square feet and a base of 9 feet. What is the height of the parallelogram?

We start by working backwards. We get the area by multiplying, so we can take the area and divide by the given base measurement.

54 $\div$ 9 $=$ 6

The measurement of the height is 6 feet.

Practice a few of these on your own. Find the missing height or base using the given measurements.

#### Example A

Area = 25 square meters

Base = 5 meters

Solution: The height is 5 meters.

#### Example B

Area = 81 square feet

Base = 27 feet

Solution: The height is 3 feet.

#### Example C

Area = 36 square inches

Height = 2 inches

Solution: The base is 18 inches.

Now back to Jillian and the quilt squares. Here is the original problem once again.

Jillian loves watching the other women work on their quilt squares. One of the ladies, Marie, came with her quilt pattern already cut out. The quilt square was designed to be filled with parallelograms and triangles.

"How much material are you using for one parallelogram?" Jillian asked her.

"I am using 18 square inches of material," Marie told Jillian.

Jillian watched her measure the length of the base of the parallelogram and noticed that it was 6 inches long.

"Hmmm," thought Jillian. "Now I can figure out the height of the parallelogram."

To figure this out, we have to divide the given area by the given base. This will give us the height.

18 $\div$ 6 $=$ 3

The height of the parallelogram is 3 inches.

### Vocabulary

Area
the space within the perimeter of a figure or place. Area often refers to the surface or covering, the middle of a figure. Area is measured in square units.
Parallelogram
a quadrilateral with two pairs of opposite congruent sides.
Rectangle
a parallelogram with two pairs of opposite congruent sides and four 90 degree angles.

### Guided Practice

Here is one for you to try on your own.

The area of the parallelogram is 169 square feet. The length of the base is 13 inches. What is the height?

To figure this out, we have to divide the given area by the length of the base. This will give us the height.

169 $\div$ 13 $=$ 13

The height of the parallelogram is 13 inches.

### Practice

Directions: Use the given area and other dimension to find the missing base or height.

1. Area = 22 sq. inches

Base = 11 inches

2. Area = 50 sq. miles

Base = 10 miles

3. Area = 48 sq. inches

Base = 8 inches

4. Area = 30 sq. meters

Base = 15 meters

5. Area = 45 sq. feet

Height = 3 feet

6. Area = 88 sq. feet

Height = 8 feet

7. Area = 121 sq. feet

Height = 11 feet

8. Area = 160 sq. miles

Height = 20 miles

9. Area = 90 sq. meters

Height = 30 meters

10. Area = 100 sq. feet

Base = 25 feet

11. Area = 120 sq. feet

Base = 20 feet

12. Area = 144 sq. feet

Base = 12 feet

13. Area = 200 sq. feet

Base = 20 feet

14. Area = 400 sq. feet

Base = 200 feet

15. Area = 360 sq. feet

Base = 100 feet