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ISEE Lower Level Math : How to find the area of a square

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Example Questions

Example Question #11 : How To Find The Area Of A Square

The perimeter of a square is 44 inches. What is the area?

Possible Answers:

$121\ \text{in}^2$

$111\ \text{in}^2$

$101\ \text{in}^2$

$88\ \text{in}^2$

$132\ \text{in}^2$

Correct answer:

$121\ \text{in}^2$

Explanation:

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

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

To find the length of one side, we divide the perimeter by 4 (since there are 4 sides of the square).

P=s+s+s+s=4s

$s=P\div4$

We know the perimeter, allowing us to solve for the side.

$s=44\div4$

s=11

This gives us 11, so we know that each side is 11 inches long. Now we can find the area.

$A=s\times s=11\times 11=121$

The area, 11 inches times 11 inches, is 121 square inches, the correct answer.

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Example Question #213 : Plane Geometry

A square has an area of 49 square inches. What is the length of one side of the square?

Possible Answers:

$4\ \text{in}$

$7\ \text{in}$

$8\ \text{in}$

$3.5\ \text{in}$

$9\ \text{in}$

Correct answer:

$7\ \text{in}$

Explanation:

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

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

Given that the area is 49 square inches, the length of one side of square would be 7, because 7 times 7 is 49.

$49=s\times s$

$49=7\times7$

s=7

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Example Question #12 : How To Find The Area Of A Square

If the perimeter of a square is 48 inches, how many square inches are in the area?

Possible Answers:

144

112

Correct answer:

144

Explanation:

The perimeter of a square is equal to the sum of the 4 sides. Given that all the sides of a square are equal, the length of one side of the square can be found by dividing the perimeter by 4.

Given that 48 divided by 4 is equal to 12, we can now find the area. The area is equal to one side multiplied by another. The result is $12\cdot12=144$

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Example Question #13 : How To Find The Area Of A Square

If the perimeter of a square is 48 inches, what is the area?

Possible Answers:

$144 \; in^{2}$

$81 \; in^{2}$

$169 \; in^{2}$

$100 \; in^{2}$

$121 \; in^{2}$

Correct answer:

$144 \; in^{2}$

Explanation:

The perimeter of a square is given by P=4s , where is the sidelength.

Plug in the given value for the perimeter:

P=4s=48

Divide both sides by 4 to find the sidelength:

$s=12\; in$

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

Plug in the sidelength we just calculated to find the area:

$A=s^{2}=(12)^{2}=144\; in^{2}$

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Example Question #14 : How To Find The Area Of A Square

If the perimeter of a square is 40 centimeters, what is the area?

Possible Answers:

$100\; cm^{2}$

$150\; cm^{2}$

$160\; cm^{2}$

$80\; cm^{2}$

$125\; cm^{2}$

Correct answer:

$100\; cm^{2}$

Explanation:

The perimeter of a square is given by P=4s , where is the sidelength.

We know the perimeter, so we can set up an equation to find the sidelength:

P=4s=40

Divide both sides by 4 to isolate the sidelength:

$s=10\; cm$

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

We just calculated the sidelength, so now we can find the area:

$A=s^{2}=(10)^{2}=100\; cm^{2}$

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Example Question #217 : Plane Geometry

The side of a square is 2 yards long. What is the area in square feet?

Possible Answers:

$4\ \text{ft}^2$

$16\ \text{ft}^2$

$36\ \text{ft}^2$

$24\ \text{ft}^2$

$25\ \text{ft}^2$

Correct answer:

$36\ \text{ft}^2$

Explanation:

To solve this question we will need to convert units from yards to feet.

$1\ \text{yard}=3\ \text{feet}$

Our question states that each side of the square is two yards.

$2\ \text{yards}=2\times3\ \text{feet}=6\ \text{feet}$

Each side of the square is 6 feet. To find the area, we need to multiply the length of two sides.

$A=s\times s;\ s=6\ \text{ft}$

$A=(6\ \text{ft})\times(6\ \text{ft})=36\ \text{ft}^2$

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Example Question #17 : How To Find The Area Of A Square

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

Possible Answers:

$a^{2}$

Correct answer:

$a^{2}$

Explanation:

If the perimeter of a square is , this means that each side is equal to because the side of a square is equal to one-fourth of its perimeter.

The area is the product of one side multiplied by another side.

Since all sides in a square are equal, the area would be equal to multiplied by , which is:

$a\cdot a=a^{2}$

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Example Question #15 : How To Find The Area Of A Square

What is the value of $5\cdot (7-2)$ ?

Possible Answers:

Correct answer:

Explanation:

$5\cdot (7-2)$ simplies to $5\cdot 5=25$ . Therefore, 25 is the correct answer.

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Example Question #16 : How To Find The Area Of A Square

Find the area of a square whose side length is .

Possible Answers:

Correct answer:

Explanation:

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

A=s^2=s*s=1*1=1

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Example Question #17 : How To Find The Area Of A Square

Find the area of a square with side length .

Possible Answers:

Correct answer:

Explanation:

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

A=s^2=s*s=9*9=81

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All ISEE Lower Level Math Resources

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ISEE Lower Level Math : How to find the area of a square

Study concepts, example questions & explanations for ISEE Lower Level Math

All ISEE Lower Level Math Resources

Example Questions

Example Question #11 : How To Find The Area Of A Square

Example Question #213 : Plane Geometry

Example Question #12 : How To Find The Area Of A Square

Example Question #13 : How To Find The Area Of A Square

Example Question #14 : How To Find The Area Of A Square

Example Question #217 : Plane Geometry

Example Question #17 : How To Find The Area Of A Square

Example Question #15 : How To Find The Area Of A Square

Example Question #16 : How To Find The Area Of A Square

Example Question #17 : How To Find The Area Of A Square

All ISEE Lower Level Math Resources

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