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

Study concepts, example questions & explanations for SSAT Middle Level Math

varsity tutors app store varsity tutors android store

Example Questions

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

Florence wants to build a fence to surround her square garden.  The garden has an area of 16 square yards. How much fencing will she need?

Possible Answers:

\(\displaystyle 4\)

\(\displaystyle 24\)

\(\displaystyle 12\)

\(\displaystyle 8\)

\(\displaystyle 16\)

Correct answer:

\(\displaystyle 16\)

Explanation:

So this question requires you to know the formula for area for a square which is side squared.  

Thus, \(\displaystyle 16 = s^{2}\), so one side is the square root of 16, or 4.  

To figure out the perimeter, add up all of the sides of the square which are all the same (4).

\(\displaystyle 4 + 4 + 4 + 4 = 16\)

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

A square has perimeter 89.4 centimeters. What is the length of one side?

Possible Answers:

\(\displaystyle 29.8 \textrm{ cm}\)

\(\displaystyle 22.35 \textrm{ cm}\)

\(\displaystyle 24.25 \textrm{ cm}\)

\(\displaystyle 32.8 \textrm{ cm}\)

\(\displaystyle 44.7 \textrm{ cm}\)

Correct answer:

\(\displaystyle 22.35 \textrm{ cm}\)

Explanation:

A square has four sides of equal measure, so divide its perimeter by 4:

\(\displaystyle 89.4 \div 4 = 22.35 \textrm{ cm}\)

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

A square has perimeter 16 feet 4 inches. What is the length of one side?

Possible Answers:

4 feet 3 inches

4 feet 1 inch

3 feet 9 inches

3 feet 11 inches

4 feet 5 inches

Correct answer:

4 feet 1 inch

Explanation:

One foot is equal to 12 inches, so the perimeter 16 feet 4 inches is equal to \(\displaystyle 16 \times 12 + 4 = 192 + 4 = 196\) inches.

An square has four sides of equal measure, so divide its perimeter by 4:

\(\displaystyle 196 \div 4 = 49\)

To convert 49 inches to feet and inches:

\(\displaystyle 49\div 12 = 4 \textrm{ R }1\)

One side measures 4 feet 1 inch.

Example Question #3 : Squares

The length of one side of a square is \(\displaystyle 7\: cm.\) What is the perimeter of this square?

Possible Answers:

\(\displaystyle 11\: cm\)

\(\displaystyle 14\: cm\)

\(\displaystyle 4\: cm\)

\(\displaystyle 7\: cm\)

\(\displaystyle 28\: cm\)

Correct answer:

\(\displaystyle 28\: cm\)

Explanation:

The perimeter of a shape is the distance around the outside boundry of that shape.

In order to find the perimeter, add up the lengths of the sides of that shape.

Because a square has four equal sides, add \(\displaystyle 7+7+7+7\) to find the perimeter. Equivalently, multiply \(\displaystyle 7*4\).

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

Find the perimeter of the square in the figure.

Screen_shot_2014-02-26_at_3.59.38_pm 

Possible Answers:

\(\displaystyle 32.1\ \textup{cm}\)

\(\displaystyle 26.8\ \textup{cm}\)

\(\displaystyle 24.8\ \textup{cm}\)

\(\displaystyle 25.6\ \textup{cm}\)

\(\displaystyle 28.2\ \textup{cm}\)

Correct answer:

\(\displaystyle 26.8\ \textup{cm}\)

Explanation:

Finding perimeter is easiest with squares. Perimeter is the distance around the outside of the figure. There are two good ways to find the perimeter. The first and longer method of finding perimeter is simply to add up the length of each side. Thus, we would take the length of top of the square and add it to the length of the right side. We'd continue all the way around. The formula for this method could be written like so: 

top + right side + bottom + left side = perimeter.

Since a square has equal sides all around, we could also write the formulalike so:

\(\displaystyle s+s+s+s=perimeter\)

The second and easier way of finding perimeter for a square is a simplification of the first method. Instead of adding the same number four times we could simply multiply by 4. Written as a formula, this would look like this:

\(\displaystyle 4\ \times \ s=perimeter\)

For the this question, your work should then look like one of these two options:

\(\displaystyle 6.7cm + 6.7cm + 6.7cm + 6.7cm = 26.8cm\)

or

\(\displaystyle 6.7cm \times 4 = 26.8cm\)

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

Find the perimeter of the square in the figure.

 Screen_shot_2014-02-26_at_4.07.44_pm

Possible Answers:

\(\displaystyle 29.2\ \textup{cm}\)

\(\displaystyle 31.6\ \textup{cm}\)

\(\displaystyle 30.4\ \textup{cm}\)

\(\displaystyle 28.8\ \textup{cm}\)

\(\displaystyle 26.9\ \textup{cm}\)

Correct answer:

\(\displaystyle 29.2\ \textup{cm}\)

Explanation:

Finding perimeter is easiest with squares. Perimeter is the distance around the outside of the figure. There are two good ways to find the perimeter. The first and longer method of finding perimeter is simply to add up the length of each side. Thus, we would take the length of top of the square and add it to the length of the right side. We'd continue all the way around. The formula for this method could be written like so: 

top + right side + bottom + left side = perimeter.

Since a square has equal sides all around, we could also write the formulalike so:

\(\displaystyle s+s+s+s=perimeter\)

The second and easier way of finding perimeter for a square is a simplification of the first method. Instead of adding the same number four times we could simply multiply by 4. Written as a formula, this would look like this:

\(\displaystyle 4\ \times \ s=perimeter\)

For the this question, your work should then look like one of these two options:

\(\displaystyle 7.3cm + 7.3cm + 7.3cm + 7.3cm = 29.2cm\)

or

\(\displaystyle 7.3cm \times 4 = 29.2cm\)

Example Question #41 : Plane Geometry

Find the perimeter of the square in the figure. 

Screen_shot_2014-02-26_at_4.10.45_pm

Possible Answers:

\(\displaystyle 34.0\ \textup{cm}\)

\(\displaystyle 26.4\ \textup{cm}\)

\(\displaystyle 28.8\ \textup{cm}\)

\(\displaystyle 30.8\ \textup{cm}\)

\(\displaystyle 32.4\ \textup{cm}\)

Correct answer:

\(\displaystyle 30.8\ \textup{cm}\)

Explanation:

Finding perimeter is easiest with squares. Perimeter is the distance around the outside of the figure. There are two good ways to find the perimeter. The first and longer method of finding perimeter is simply to add up the length of each side. Thus, we would take the length of top of the square and add it to the length of the right side. We'd continue all the way around. The formula for this method could be written like so: 

top + right side + bottom + left side = perimeter.

Since a square has equal sides all around, we could also write the formulalike so:

\(\displaystyle s+s+s+s=perimeter\)

The second and easier way of finding perimeter for a square is a simplification of the first method. Instead of adding the same number four times we could simply multiply by 4. Written as a formula, this would look like this:

\(\displaystyle 4\ \times \ s=perimeter\)

For the this question, your work should then look like one of these two options:

\(\displaystyle 7.7cm + 7.7cm + 7.7cm + 7.7cm = 30.8cm\)

or

\(\displaystyle 7.7cm \times 4 = 30.8cm\)

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

Find the perimeter of the square in the figure.

 Screen_shot_2014-02-26_at_4.13.19_pm

Possible Answers:

\(\displaystyle 30.5\ \textup{cm}\)

\(\displaystyle 29.6\ \textup{cm}\)

\(\displaystyle 32.4\ \textup{cm}\)

\(\displaystyle 32.5\ \textup{cm}\)

\(\displaystyle 34.4\ \textup{cm}\)

Correct answer:

\(\displaystyle 32.4\ \textup{cm}\)

Explanation:

Finding perimeter is easiest with squares. Perimeter is the distance around the outside of the figure. There are two good ways to find the perimeter. The first and longer method of finding perimeter is simply to add up the length of each side. Thus, we would take the length of top of the square and add it to the length of the right side. We'd continue all the way around. The formula for this method could be written like so: 

top + right side + bottom + left side = perimeter.

Since a square has equal sides all around, we could also write the formulalike so:

\(\displaystyle s+s+s+s=perimeter\)

The second and easier way of finding perimeter for a square is a simplification of the first method. Instead of adding the same number four times we could simply multiply by 4. Written as a formula, this would look like this:

\(\displaystyle 4\ \times \ s=perimeter\)

For the this question, your work should then look like one of these two options:

\(\displaystyle 8.1cm + 8.1cm + 8.1cm + 8.1cm = 32.4cm\)or

\(\displaystyle 8.1cm \times 4 = 32.4cm\)

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

Find the perimeter of the square in the figure. 

Screen_shot_2014-02-26_at_4.15.43_pm

Possible Answers:

\(\displaystyle 38.2\ \textup{cm}\)

\(\displaystyle 34.4\ \textup{cm}\)

\(\displaystyle 29.2\ \textup{cm}\)

\(\displaystyle 32.6\ \textup{cm}\)

\(\displaystyle 36.9\ \textup{cm}\)

Correct answer:

\(\displaystyle 34.4\ \textup{cm}\)

Explanation:

Finding perimeter is easiest with squares. Perimeter is the distance around the outside of the figure. There are two good ways to find the perimeter. The first and longer method of finding perimeter is simply to add up the length of each side. Thus, we would take the length of top of the square and add it to the length of the right side. We'd continue all the way around. The formula for this method could be written like so: 

top + right side + bottom + left side = perimeter.

Since a square has equal sides all around, we could also write the formulalike so:

\(\displaystyle s+s+s+s=perimeter\)

The second and easier way of finding perimeter for a square is a simplification of the first method. Instead of adding the same number four times we could simply multiply by 4. Written as a formula, this would look like this:

\(\displaystyle 4\ \times \ s=perimeter\)

For the this question, your work should then look like one of these two options:

\(\displaystyle 8.6cm + 8.6cm + 8.6cm + 8.6cm = 34.4 cm\)

or

\(\displaystyle 8.6cm \times 4 = 34.4 cm\)

Example Question #10 : Squares

Find the perimeter of the square in the figure.

Screen_shot_2014-02-26_at_4.18.05_pm

Possible Answers:

\(\displaystyle 35.6\ \textup{cm}\)

\(\displaystyle 38.4\ \textup{cm}\)

\(\displaystyle 36.4\ \textup{cm}\)

\(\displaystyle 37.2\ \textup{cm}\)

\(\displaystyle 34.8\ \textup{cm}\)

Correct answer:

\(\displaystyle 36.4\ \textup{cm}\)

Explanation:

Finding perimeter is easiest with squares. Perimeter is the distance around the outside of the figure. There are two good ways to find the perimeter. The first and longer method of finding perimeter is simply to add up the length of each side. Thus, we would take the length of top of the square and add it to the length of the right side. We'd continue all the way around. The formula for this method could be written like so: 

top + right side + bottom + left side = perimeter.

Since a square has equal sides all around, we could also write the formulalike so:

\(\displaystyle s+s+s+s=perimeter\)

The second and easier way of finding perimeter for a square is a simplification of the first method. Instead of adding the same number four times we could simply multiply by 4. Written as a formula, this would look like this:

\(\displaystyle 4\ \times \ s=perimeter\)

For the this question, your work should then look like one of these two options:

\(\displaystyle 9.1cm + 9.1cm + 9.1cm + 9.1cm = 36.4 cm\)

or

\(\displaystyle 9.1cm \times 4 = 36.4 cm\)

Learning Tools by Varsity Tutors