# ACT Math : How to find the perimeter of a parallelogram

## Example Questions

### Example Question #1 : How To Find The Perimeter Of A Parallelogram

A parallelogram, with dimensions in cm, is shown below.

What is the perimeter of the parallelogram, in cm?

Explanation:

The triangle on the left side of the figure has a and a  angle. Since all of the angles of a triangle must add up to , we can find the angle measure of the third angle:

Our third angle is and we have a triangle.

A triangle has sides that are in the corresponding ratio of . In this case, the side opposite our angle is , so

We also now know that

Now we know all of our missing side lengths.  The right and left side of the parallelogram will each be . The bottom and top will each be . Let's combine them to find the perimeter:

### Example Question #1 : How To Find The Perimeter Of A Parallelogram

Note: Figure NOT drawn to scale.

Give the perimeter of Parallelogram  in the above diagram.

Explanation:

By the 30-60-90 Theorem, the length of the short leg of  is the length of the long leg divided by , so

Its hypotenuse has twice the length of the short leg, so

The perimeter of the parallelogram is

### Example Question #2 : How To Find The Perimeter Of A Parallelogram

Note: Figure NOT drawn to scale.

Give the perimeter of Parallelogram  in the above diagram.

Explanation:

By the 45-45-90 Theorem, the lengths of the legs of are equal, so

Its hypotenuse has measure  that of the common measure of its legs, so

The perimeter of the parallelogram is

### Example Question #3 : How To Find The Perimeter Of A Parallelogram

Note: Figure NOT drawn to scale.

To the nearest tenth, give the perimeter of Parallelogram  in the above diagram.

Explanation:

The perimeter of the parallelogram is

### Example Question #4 : How To Find The Perimeter Of A Parallelogram

In the above figure, Parallelogram  has area 100. To the nearest tenth, what is its perimeter?

Explanation:

By the 45-45-90 Theorem, . Since  and  are its base and height:

Also by the 45-45-90 Theorem,

The perimeter of the parallelogram is

### Example Question #1 : How To Find The Perimeter Of A Parallelogram

In the above figure, Parallelogram  has area 100. To the nearest tenth, what is its perimeter?

Explanation:

By the 30-60-90 Theorem,

The area of the parallelogram is the product of height  and base , so

Also by the 30-60-90 Theorem,

The perimeter of the parallelogram is

### Example Question #6 : How To Find The Perimeter Of A Parallelogram

Note: Figure NOT drawn to scale.

In the above figure, Parallelogram  has area 100. To the nearest tenth, what is its perimeter?