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ISEE Middle Level Math : Squares

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Example Questions

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

What is the area of a square if the length of one side is $\sqrt{3}$ ?

Possible Answers:

$\frac{1}{3}$

$3\sqrt{3}$

$\sqrt{3}$

Correct answer:

Explanation:

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

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

We are given the side length, allowing us to solve.

$s=\sqrt{3}$

$A=(\sqrt{3})^2=3$

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

A square has an area of 36, and each side is equal to What is the value of ?

Possible Answers:

Correct answer:

Explanation:

Each side of a square is equal to the square root of the area. The square root of 36 is 6, so each side is 6. Thus, 3x (being a side of the square is equal to 6. This means that x is equal to 2 because 3 times 2 is 6.

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

Find the area of a square with side length 10.

Possible Answers:

1000

100

Correct answer:

100

Explanation:

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

A=s^2=10^2=10*10=100

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

The area of a square is 4*side ?

Possible Answers:

False

True

Correct answer:

False

Explanation:

The area of a square is the side length squared not the side length times .

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

If you are given one side length of a square, you can find the area with that information.

Possible Answers:

True

False

Correct answer:

True

Explanation:

To find the area of a square, you multiple length * width . But with a square all the sides are equal so the equation really is 2* side or the side length squared. Since you are given the side length, you can find the area.

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

A new building in New York City will have a footprint that is a perfect square, taking up a complete city block. If one city block is of a mile, what is the area taken up by the building?

Possible Answers:

$\frac{1}{4}mi^2$

$\frac{1}{64}mi^2$

$\frac{1}{16}mi^2$

$\frac{1}{2} mi^2$

Correct answer:

$\frac{1}{64}mi^2$

Explanation:

A new building in New York City will have a footprint that is a perfect square, taking up a complete city block. If one city block is of a mile, what is the area taken up by the building?

Find the area of a square by raising the side length to the second power:

$A=s^2=\frac{1}{8}^2=\frac{1}{8}*\frac{1}{8}=\frac{1}{64}mi^2$

So our area is:

$\frac{1}{64}mi^2$

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

Use the following to answer the question.

Square1

Find the area of the square.

Possible Answers:

$36\text{ft}^2$

$12\text{ft}^2$

$24\text{ft}$

$24\text{ft}^2$

$36\text{ft}$

Correct answer:

$36\text{ft}^2$

Explanation:

When finding the area of a square, we use the following formula:

$\text{area of square} = l \cdot w$

where l is the length and w is the width of the square.

Now, we know that a square has 4 equal sides. So given the square

Square1

we know the length is 6ft and the width is 6ft. So, we can substitute into the formula.

$\text{area of square} = 6\text{ft} \cdot 6\text{ft}$

$\text{area of square} = 36\text{ft}^2$

Note that the label is also squared. This is because when we multiply, we are also multiplying the label.

$\text{ft} \cdot \text{ft} = \text{ft}^2$

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

Find the area of a square with a width of 8 inches.

Possible Answers:

$64 \text{ inches}$

$32 \text{ inches}$

$32 \text{ inches}^2$

$\text{There is not enough information to answer the question.}$

$64 \text{ inches}^2$

Correct answer:

$64 \text{ inches}^2$

Explanation:

To find the perimeter of a square, we use the following formula:

$\text{area of square} = l \cdot w$

where l is the length and w is the width of the square.

Now, we know the width of the square is 8 inches. Because it is a square, we know that all sides are equal. Therefore, the length is also 8 inches. Knowing this, we can substitute into the formula. We get

$\text{area of square} = 8 \text{ inches} \cdot 8 \text{ inches}$

$\text{area of square} = 64 \text{ inches}^2$

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

You are playing Monopoly and notice that the dice is a cube. If the dice has a height of 2 centimeters, what is the area of one of its surfaces?

Possible Answers:

4cm^2

8cm^2

12cm^2

16cm^2

Correct answer:

4cm^2

Explanation:

You are playing Monopoly and notice that the dice is a cube. If the dice has a height of 2 centimeters, what is the area of one of its surfaces?

We can begin by realizing that we need to find the area of just one surface of the cube. This surface will be a square, we know this because we are dealing with a cube.

So, we need to find the area of a square. Easy enough with the following formula:

$A_{square}=s^2$

Now, we just need to know "s." To find s, we need to look at the question. We are told that the height of the cube is 2cm. This means that the side length of our base (square) is also 2.

So...

$A_{square}=(2cm)^2=4cm^2$

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

Find the area of a square with a base of 9 inches.

Possible Answers:

$\text{There is not enough information to answer the question.}$

$36\text{in}$

$36\text{in}^2$

$81\text{in}^2$

$81\text{in}$

Correct answer:

$81\text{in}^2$

Explanation:

To find the area of a square, we will use the following formula:

$\text{area of square} = l \cdot w$

where l is the length and w is the width of the square.

Now, we know the square has a base of length 9 inches. Because it is a square, we know that all sides are equal. This means all sides are 9 inches. Therefore, the width is also 9 inches. Knowing this, we can substitute into the formula. So,

$\text{area of square} = 9\text{in} \cdot 9\text{in}$

$\text{area of square} = 81\text{in}^2$

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : Squares

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

All ISEE Middle Level Math Resources

Example Questions

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

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

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

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

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

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

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 #15 : How To Find The Area Of A Square

All ISEE Middle Level Math Resources

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