# SSAT Upper Level Math : How to find the perimeter of a parallelogram

## Example Questions

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

The base length of a parallelogram is which is two times more than its side length. Give the perimeter of the parallelogram in terms of .

Explanation:

The side length is half of the base length:

The perimeter of a parallelogram is:

Where:

is the base length of the parallelogram and is the side length

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

The side length of a parallelogram is and the base length is three times more than side length. Give the perimeter of the parallelogram in terms of .

Explanation:

The base length is three times more than the side length, so we have:

Base length

The perimeter of a parallelogram is:

Where:

is the base length of the parallelogram and  is the side length. So we get:

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

The base length of a parallelogram is 10 inches and the side length is 6 inches. Give the perimeter of the parallelogram.

Explanation:

Like any polygon, the perimeter of a parallelogram is the total distance around the outside, which can be found by adding together the length of each side. In case of a parallelogram, each pair of opposite sides is the same length, so the perimeter is twice the base plus twice the side length. Or as a formula we can write:

Where:

is the base length of the parallelogram and is the side length. So we can write:

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

The base length of a parallelogram is . If the perimeter of the parallelogram is 24, give the side length in terms of .

Explanation:

Let:

Side length .

The perimeter of a parallelogram is:

where:

is the base length of the parallelogram and is the side length. The perimeter is known, so we can write:

Now we solve the equation for :

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

The base length of a parallelogram is identical to its side length. If the perimeter of the parallelogram is 40, give the base length.

Explanation:

The perimeter of a parallelogram is:

Where:

is the base length of the parallelogram and  is the side length. In this problem the base length and side length are identical, that means:

So we can write:

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

The base length of a parallelogram is and the side length is . Give the perimeter of the parallelogram in terms of  and calculate it for .

Explanation:

The perimeter of a parallelogram is:

where:

is the base length of the parallelogram and  is the side length. So we have:

and:

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

The above parallelogram has area 100. Give its perimeter.

Explanation:

The height of the parallelogram is , and the base is . By the  Theorem, . Since the product of the height and the base of a parallelogram is its area,

By the  Theorem,

, and

The perimeter of the parallelogram is

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

Give the perimeter of the above parallelogram if .