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

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Example Questions

Example Question #21 : Geometry

Which of the following is equal to the area of a square with perimeter 8 meters?

Possible Answers:

$40,000 \textrm{ cm}^{2}$ $\displaystyle 40,000 \textrm{ cm}^{2}$

$80,000 \textrm{ cm}^{2}$ $\displaystyle 80,000 \textrm{ cm}^{2}$

$160,000 \textrm{ cm}^{2}$ $\displaystyle 160,000 \textrm{ cm}^{2}$

$20,000 \textrm{ cm}^{2}$ $\displaystyle 20,000 \textrm{ cm}^{2}$

Correct answer:

$40,000 \textrm{ cm}^{2}$ $\displaystyle 40,000 \textrm{ cm}^{2}$

Explanation:

The sidelength of a square is one-fourth its perimeter, so the sidelength here is one-fourth of 8, or 2, meters. One meter is equal to 100 centimeters, so the sidelength is 200 centimeters. Square this to get the area:

$200 ^{2} = 200 \times 200 = 40,000$ $\displaystyle 200 ^{2} = 200 \times 200 = 40,000$ square centimeters.

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Example Question #22 : Geometry

Which of the following is the area of a square with perimeter 7 feet?

Possible Answers:

$729 \textrm{ in}^{2}$ $\displaystyle 729 \textrm{ in}^{2}$

$441 \textrm{ in}^{2}$ $\displaystyle 441 \textrm{ in}^{2}$

$961 \textrm{ in}^{2}$ $\displaystyle 961 \textrm{ in}^{2}$

$529 \textrm{ in}^{2}$ $\displaystyle 529 \textrm{ in}^{2}$

Correct answer:

$441 \textrm{ in}^{2}$ $\displaystyle 441 \textrm{ in}^{2}$

Explanation:

Convert 7 feet to inches by multiplying by 12: $7 \times 12 = 84$ $\displaystyle 7 \times 12 = 84$ inches.

The sidelength of a square is one-fourth its perimeter, so the sidelength here is one-fourth of 84 inches. This is $84 \div 4 = 21$ $\displaystyle 84 \div 4 = 21$ inches.

Square this to get the area:

$21 ^{2} = 21 \times 21 = 441$ $\displaystyle 21 ^{2} = 21 \times 21 = 441$ square inches

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

What is the area of a square with a side length of 4?

Possible Answers:

Correct answer:

Explanation:

The area of a square is represented by the equation $\dpi{100} Area = side^{2}$ $\displaystyle \dpi{100} Area = side^{2}$.

Therefore the area of this square is $\dpi{100} 4^{2}=16$ $\displaystyle \dpi{100} 4^{2}=16$.

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

Square A has sides measuring 5 meters. A second square, Square B, has sides that are 2 meters longer than the sides of Square A. What is the difference in area of Square A and Square B?

Possible Answers:

$49\ m^2$ $\displaystyle 49\ m^2$

$24\ m^{2}$ $\displaystyle 24\ m^{2}$

$8\ m^2$ $\displaystyle 8\ m^2$

$9\ m^2$ $\displaystyle 9\ m^2$

$21\ m^2$ $\displaystyle 21\ m^2$

Correct answer:

$24\ m^{2}$ $\displaystyle 24\ m^{2}$

Explanation:

The area of Square A is 5 * 5, or 25 m².

Since each of Square B's sides is 2 meters longer, the sides measure 7 meters. Therefore, the area of square B is 49 m².

Subtract to find the difference in areas: $49-25=24\ m^2$ $\displaystyle 49-25=24\ m^2$

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

The ratio of the length of a side of one square to the length of the side of another square is $\frac{a}{b}$ $\displaystyle \frac{a}{b}$. Give the ratio of the area of the second square to the area of the first square.

Possible Answers:

$\displaystyle 2$

$\frac{b^2}{a}$ $\displaystyle \frac{b^2}{a}$

$\frac{a^2}{b^2}$ $\displaystyle \frac{a^2}{b^2}$

$\frac{b^2}{a^2}$ $\displaystyle \frac{b^2}{a^2}$

$\frac{b}{a^2}$ $\displaystyle \frac{b}{a^2}$

Correct answer:

$\frac{b^2}{a^2}$ $\displaystyle \frac{b^2}{a^2}$

Explanation:

The area of a square can be found as follows:

$\displaystyle Area=x^2$

Where:

$x=Side\ Length$ $\displaystyle x=Side\ Length$

So we can write:

$\frac{Area\ 2}{Area\ 1}=\frac{b^2}{a^2}$ $\displaystyle \frac{Area\ 2}{Area\ 1}=\frac{b^2}{a^2}$

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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 $\sqrt{3}$ $\displaystyle \sqrt{3}$?

Possible Answers:

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$\displaystyle 3$

$3\sqrt{3}$ $\displaystyle 3\sqrt{3}$

$\displaystyle 9$

$\sqrt{3}$ $\displaystyle \sqrt{3}$

Correct answer:

$\displaystyle 3$

Explanation:

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

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

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

$s=\sqrt{3}$ $\displaystyle s=\sqrt{3}$

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

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

A square has an area of 36, and each side is equal to $\displaystyle 3x$ What is the value of $\displaystyle x$?

Possible Answers:

$\displaystyle 3$

$\displaystyle 6$

$\displaystyle 2$

$\displaystyle 4$

Correct answer:

$\displaystyle 2$

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 #5 : How To Find The Area Of A Square

Find the area of a square with side length 10.

Possible Answers:

100 $\displaystyle 100$

$\displaystyle 40$

1000 $\displaystyle 1000$

$\displaystyle 50$

Correct answer:

100 $\displaystyle 100$

Explanation:

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

$\displaystyle A=s^2=10^2=10*10=100$

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Example Question #1951 : Isee Middle Level (Grades 7 8) Mathematics Achievement

The area of a square is 4*side $\displaystyle 4*side$?

Possible Answers:

False $\displaystyle False$

True $\displaystyle True$

Correct answer:

False $\displaystyle False$

Explanation:

The area of a square is the side length squared not the side length times $\displaystyle 4$.

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Example Question #4 : 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 $\displaystyle length * width$. But with a square all the sides are equal so the equation really is 2* side $\displaystyle 2* side$ or the side length squared. Since you are given the side length, you can find the area.

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All ISEE Middle Level Math Resources

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

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #21 : Geometry

Example Question #22 : Geometry

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

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

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

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

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

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

Example Question #1951 : Isee Middle Level (Grades 7 8) Mathematics Achievement

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

All ISEE Middle Level Math Resources

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