How to find the perimeter of a square - ISEE Lower Level Quantitative Reasoning

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Question

If the area of a square is 100 cm2 then what is the length of each side? What is the perimeter of the square?

Answer

The given area of the square was calculated by multiplying the measurement of one side of the square by the measurement of another side of the square (which are equal measurements). Since the area was 100 cm then there was a number when multiplied to itself would be 100. The number that makes this true is 10 as

$10\times 10=100$

It is now known that each side of the square has a length of 10 cm and to find the perimeter of the square the length of each side must be used to find the total length around the square. Therefore, since each side is 10 cm then the perimeter can be found by adding all of the sides which would be

The perimeter of the square would be

$40\ cm$

This makes the correct answer

$10\ cm: 40\ cm$

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Question

What is the perimeter of the square below?

$\huge \dpi{300} \fn_cm \huge \square$

Answer

To find the perimeter of a shape, take all of the outside measurements and add them together. There are only 2 measurements showing. However, perimeter goes all the way around the square which has four equal sides. Therefore, the measurement of the other sides must be the same and must be used to find the perimeter.

Take all four sides and add them together to find the perimeter of the square. Since each side is equally 5 inches then the total of the sides (or perimeter of the square) would be

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Question

Use the square to answer the question.

What is the perimeter of the square?

Answer

To find the perimeter of a square, add all the sides together:

$7\textup{ ft}+7\textup{ ft}+7\textup{ ft}+7\textup{ ft}=28\textup{ ft}$

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Question

What is the perimeter of a square that has a side with a length of 12 cm.?

Answer

To find the perimeter of a shape, you must add up the lengths of the sides. By definition, a square has 4 equal sides. So, you only need to know the length of one side of a square in order to know the lengths of all the sides of a square.

Since the length of one side of this square is 12 cm., you can either add the lengths of the four sides together or multiply the length of one side by 4.

The units used in this answer would be cm. — not cm.2 — because we are only find the length aroud the shape when solving for perimeter.

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Question

If the perimeter of a square is

What is the length of one of its sides?

Answer

The perimeter of a shape is equal to the sum of the lengths of each side. By definition, a square has 4 equal sides. As a result, you can divde the perimeter by 4 to get the length of one side:

$\frac{44}{4}=11$

Since divided by equals , then is the length of one side of the square.

You can also check your answer by adding up the lengths of all the sides or by multiplying the length of one of the sides by . If you get , you are correct.

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Question

If the area of a square is $81; cm^{2}$ , what is the perimeter?

Answer

The area of a square is given by $A=s^{2}$ , where is the sidelength.

Plug in the given information:

$A=81=s^{2}$

Take the square root of both sides:

The perimeter of a square is given by , where is again the sidelength.

Plug in the sidelength that we just calculated:

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Question

If the area of a square is $144; in^{2}$ , what is the perimeter?

Answer

The area of a square is given by $A=s^{2}$ , where is the sidelength.

Plug in the perimeter given in the question:

$A=144=s^{2}$

Take the square root of both sides:

The perimeter of a square is given by , where is again the sidelength.

Plug the sidelength we just calculated into the perimeter formula:

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Question

The area of a square is $64; cm^{2}$ . What is the perimeter?

Answer

The area of a square is given by $A=s^{2}$ , or $s^{2} = 64$ . Take the square root of both sides to get .

The perimeter of a square is given by . Substitute the value obtained from the area equation to get

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Question

The area of a square is $49; cm^{2}$ . What is the perimeter?

Answer

The area of a square is given by $A=s^{2}$ , or $s^{2} = 49$ . Take the square root of both sides to get .

The perimeter of a square is given by . Substitute the side length obtained from the area equation to get

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Question

The area of a square is $36; in^{2}$ . What is the perimeter?

Answer

The area of a square is given by $A=s^{2}$ . Here $s^{2} = 36$ , so take the square root of both sides to get .

The perimeter of a square is given by . Substitute the side length obtained from the area equation to get

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Question

The area of a square is $100; in^{2}$ . What is the perimeter?

Answer

The area of a square is given by $A=s^{2}$ , or $s^{2} = 100$ . Take the square root of both sides to get .

The perimeter of a square is given by . Substitute the side length obtained from the area equation to get .

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Question

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

Answer

The area of a square is calculated by multiplying one side by itself.

$A=s\times s$

If the area is 25, then the length of one side will be the square root of 25.

$s=\sqrt{25}=5$

The square root of 25 is 5, so each side must be 5 feet long.

If each of the four sides is 5 feet long, then the perimeter would be 20 feet because there are four sides total.

$P=s+s+s+s=4\times s$

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Question

Billy built a $25\ \text{ft}^2$ enclosure for his puppy in his backyard, in the shape of a square. One side consisted of the wall of his home, while the other three sides consisted of a fence that he built. How many feet of fence did Billy build?

Answer

The area of a square is the product of one side times another side. Since the sides of a square are equal lengths, this is equal to:

$A=s\times s=s^2$

Given that the area was 25 square feet, one side would be the square root of 25 (given that all sides of a square are equaly).

$s=\sqrt{25}=5$

The square root of 25 is 5, which would be the length of one side. Since one side of the enclosure is the wall of Billy's home, Billy only had to build 3 additional sides, each of length 5.

$5+5+5=3\times5=15$

Since 3 times 5 is 15, the correct answer is 15.

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Question

If a square has an area of 100 square feet, what is the perimeter?

Answer

When you have the area of a square, you can deduce the length of the sides by taking the square root of the area.

$A=s\times s=s^2$

$s=\sqrt{A}$

Given that the area is 100 square feet, and that the square root of 100 is 10, each side is 10 feet.

$s=\sqrt{100\text{ft}^2}=10\text{ft}$

With 4 sides, that means that the perimeter of a square would be 4 times 10, which is 40.

$P=4\times10\text{ft}=40\ \text{ft}$

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Question

Which of the following is the perimeter of a square that has an area of 9 square inches?

Answer

If a square has an area of 9 square inches, each side is 3 inches. This is because 3 inches times 3 inches is 9 inches. (The formula for the area of a square is length times hieght.)

Given that a square has 4 sides, we get the perimeter by multiplying 3 by 4, giving us a perimeter of 12 inches.

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Question

If the length of one side of a square is equal to , what is the value of the perimeter?

Answer

The perimeter of a square is equal to the sum of all of its sides.

If a side is , that means the perimeter would be equal to a value of , which is the equivalent of ; the correct answer.

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Question

Debby has a square piece of paper that has an area of 36. What is its perimeter?

Answer

For a square, all four sides are equal, and the area is calculated by multiplying one side by itself.

$A=s\times s$

Since the area of the square is 36, we know that one side would be equal to 6 because $6\times6=36$ .

$36=s\times s=6\times 6$

Since each side is 6, the perimeter would be calculated by adding these four sides together.

This would give us:

Or

$6\times4=24$

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Question

What type of a shape always has 4 equal sides?

Answer

Squares, rhombuses, rectangles, and quadrilaterals all have four sides, but only squares and rhombuses have four equal sides.A square also has four equal angles (right angles), while a rhombus has two pairs of congruent angles.

A rectangle has four equal angles and two pairs of congruent sides. A quadrilateral refers to any four-sided shape.

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Question

If the area of a square is 81, what is the perimeter?

Answer

If the area of a square is 81, the length of one side can be found by taking the square root. Given that the square root of 81 is 9, the length of a side of the square is 9.

The perimeter is the sum of all four sides. Therefore, the perimeter is .

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Question

Find the perimeter of a square whose side length is .

Answer

To solve, simply use the formula for the perimeter of a square. Thus,

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