ISEE Lower Level Math : Squares

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

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Example Questions

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

A square has a perimeter of 24 inches. What is the area of the square?

Possible Answers:

\displaystyle 36\text{in}^2

\displaystyle 12\text{in}^2

\displaystyle 72\text{in}^2

\displaystyle 24\text{in}^2

\displaystyle 6\text{in}^2

Correct answer:

\displaystyle 36\text{in}^2

Explanation:

Given that all four sides of a square are equal, if the perimeter is 24 inches, then you need to divide by 4 to find the length of each side.

\displaystyle P=s+s+s+s=4s

\displaystyle P=24

\displaystyle P\div4=s

\displaystyle 24\text{in}\div4=6\text{in}

The area is found by multiplying two sides together.

\displaystyle A=s\times s

Plug in the value of \displaystyle s to solve.

\displaystyle 6\text{in}\times 6\text{in} = 36\text{in}^2

Therefore, \displaystyle 36\text{in}^2 is the correct answer. 

Example Question #231 : Geometry

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

Possible Answers:

\displaystyle 121\ \text{in}^2

\displaystyle 111\ \text{in}^2

\displaystyle 101\ \text{in}^2

\displaystyle 88\ \text{in}^2

\displaystyle 132\ \text{in}^2

Correct answer:

\displaystyle 121\ \text{in}^2

Explanation:

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

\displaystyle 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).

\displaystyle P=s+s+s+s=4s

\displaystyle s=P\div4

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

\displaystyle s=44\div4

\displaystyle s=11

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

\displaystyle A=s\times s=11\times 11=121

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

 

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:

\displaystyle 4\ \text{in}

\displaystyle 7\ \text{in}

\displaystyle 8\ \text{in}

\displaystyle 3.5\ \text{in}

\displaystyle 9\ \text{in}

Correct answer:

\displaystyle 7\ \text{in}

Explanation:

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

\displaystyle 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. 

\displaystyle 49=s\times s

\displaystyle 49=7\times7

\displaystyle s=7

Example Question #211 : Plane Geometry

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

Possible Answers:

\displaystyle 144

\displaystyle 112

\displaystyle 98

\displaystyle 36

Correct answer:

\displaystyle 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 \displaystyle 12\cdot12=144

Example Question #212 : Plane Geometry

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

Possible Answers:

\displaystyle 81 \; in^{2}

\displaystyle 144 \; in^{2}

\displaystyle 100 \; in^{2}

\displaystyle 169 \; in^{2}

\displaystyle 121 \; in^{2}

Correct answer:

\displaystyle 144 \; in^{2}

Explanation:

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

Plug in the given value for the perimeter:

\displaystyle P=4s=48 

Divide both sides by 4 to find the sidelength:

\displaystyle s=12\; in

The area of a square is given by \displaystyle A=s^{2}

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

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

Example Question #234 : Geometry

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

Possible Answers:

\displaystyle 80\; cm^{2}

\displaystyle 125\; cm^{2}

\displaystyle 150\; cm^{2}

\displaystyle 160\; cm^{2}

\displaystyle 100\; cm^{2}

Correct answer:

\displaystyle 100\; cm^{2}

Explanation:

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

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

\displaystyle P=4s=40 

Divide both sides by 4 to isolate the sidelength:

\displaystyle s=10\; cm

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

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

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

Example Question #1171 : Isee Lower Level (Grades 5 6) Mathematics Achievement

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

Possible Answers:

\displaystyle 25\ \text{ft}^2

\displaystyle 36\ \text{ft}^2

\displaystyle 16\ \text{ft}^2

\displaystyle 24\ \text{ft}^2

\displaystyle 4\ \text{ft}^2

Correct answer:

\displaystyle 36\ \text{ft}^2

Explanation:

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

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

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

\displaystyle 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.

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

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

Example Question #1171 : Isee Lower Level (Grades 5 6) Mathematics Achievement

If the perimeter of a square is \displaystyle 4a, what is the area?

Possible Answers:

\displaystyle a^{2}

\displaystyle 2a

\displaystyle 4a

\displaystyle a

Correct answer:

\displaystyle a^{2}

Explanation:

If the perimeter of a square is \displaystyle 4a, this means that each side is equal to \displaystyle a 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 \displaystyle a multiplied by \displaystyle a, which is:

\displaystyle a\cdot a=a^{2} 

Example Question #81 : Squares

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

Possible Answers:

\displaystyle 25

\displaystyle 15

\displaystyle 20

\displaystyle 10

Correct answer:

\displaystyle 25

Explanation:

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

Example Question #221 : Quadrilaterals

Find the area of a square whose side length is \displaystyle 1.

Possible Answers:

\displaystyle 1

\displaystyle 2

\displaystyle 4

\displaystyle 11

Correct answer:

\displaystyle 1

Explanation:

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

\displaystyle A=s^2=s*s=1*1=1

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