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

## Example Questions

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

The sidelength of a square is equal to . Give its perimeter in terms of .

Explanation:

The perimeter of a square is four times its sidelength, so the perimeter of this square is

.

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

Half of the side length of a square is equal to .

Give its perimeter in terms of .

Explanation:

Perimeter of a square is four times the length of a side. The half-length of each side is equal to that means the side length is equal to:

So we can write:

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

The perimeter of a square is equal to 64 meters. Give the length of each side in centimeters.

Explanation:

Perimeter of a square is four times the length of a side. The perimeter is known here and equal to 64 meters. So we can write:

where is the length of each side. So we have:

The length of each side is 16 meters. There are 100 centimeters in a meter. So we get:

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

The side length of a square is equal to . What is its perimeter in terms of  ?

Explanation:

The perimeter is the total distance around the outside, which can be found by adding together the length of each side. In the case of a square, all four sides have the same length, so the perimeter is four times the length of a side. So we can write:

Perimeter of square = , where  is the length of a side.

In this problem:

### Example Question #5 : How To Find The Perimeter Of A Square

The length of each side of the square is . What is the perimeter of the square?

Explanation:

To find the perimter of a square, multiply the side length by 4.

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

A square has a diagonal length of  units. What is its perimeter?

units

units

units

units

units

Explanation:

Since the diagonal of a squre is also the hypotenuse of a right triangle whose legs are the sides of the square, use the Pythagorean Theorem to find out the lengths of the sides of the square.

Now, multiply the side length by 4 to find the perimter.

### Example Question #7 : How To Find The Perimeter Of A Square

The area of a square is . What is the perimeter of the square?

Explanation:

To figure out the perimeter, we need to first find the length of 1 side of the square.

Find the length of a side of the square using the information given about the area.

Now, multiply the side length by 4.

### Example Question #8 : How To Find The Perimeter Of A Square

The diagonal of a square is . Find the perimeter of the square.

Explanation:

The diagonal of a square is also the hypotenuse of a triangle whose legs are two sides of the square. Using that information, we can find the length of each side of the square.

Now, multiply the side length by 4 to find the perimeter.

### Example Question #9 : How To Find The Perimeter Of A Square

The track at Harriet Beecher Stowe High School is a perfect square of with diagonal 600 feet, and is shown in the above figure. Beginning at point A, Corinne runs around the track clockwise three complete times, then contunes to run until she reaches point B. Which of the following comes closest to the distance Corinne runs?

You will need to know that .

Explanation:

A square with diagonal 600 feet will have as its sidelength

feet.

If Corinne runs the entire perimeter of the square three times, and then runs on to Point B, she will run this distance a total of about  times. This is a total of

feet.

Divide by 5,280 to convert to miles:

The closest response is 1 mile.

### Example Question #10 : How To Find The Perimeter Of A Square

The track at Frederick Douglass High School is a perfect square of with diagonal 400 feet, and is shown in the above figure. Julia wants to run around the track for one mile. If Julia starts at point A and runs clockwise, where will she be after she has run for a mile?

A hint: