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ISEE Middle Level Math : Squares

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Example Questions

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Example Question #111 :Plane Geometry

Find the perimeter of a square with a width of 9in.

Possible Answers:

$54\text{in}$

$36\text{in}$

$49\text{in}$

$28\text{in}$

$32\text{in}$

Correct answer:

$36\text{in}$

Explanation:

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

P = a+b+c+d

wherea, b, c,anddare the lengths of the sides of the square.

Now, we know the width of the square is 9in. Because it is a square, all sides are equal. Therefore, all sides are 9in. So, we can substitute.

$P = 9\text{in} + 9\text{in} + 9\text{in} + 9\text{in}$

$P = 36\text{in}$

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Example Question #112 :Plane Geometry

Find the perimeter of a square with a width of 9cm.

Possible Answers:

$54\text{cm}$

$81\text{cm}$

$27\text{cm}$

$36\text{cm}$

$18\text{cm}$

Correct answer:

$36\text{cm}$

Explanation:

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

P = a+b+c+d

wherea, b, c,anddare the lengths of the sides of the square.

Now, we know the width of the square is 9cm. Because it is a square, all sides are equal. Therefore, all sides are 9cm. So, we can substitute. We get

$P = 9\text{cm} + 9\text{cm} + 9\text{cm} + 9\text{cm}$

$P = 36\text{cm}$

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Example Question #113 :Plane Geometry

Find the perimeter of a square with a length of 6in.

Possible Answers:

$12\text{in}$

$18\text{in}$

$48\text{in}$

$24\text{in}$

$36\text{in}$

Correct answer:

$24\text{in}$

Explanation:

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

P = a+b+c+d

wherea, b, c,anddare the lengths of the sides of the square.

Now, we know the length of the square is 6in. Because it is a square, all sides are equal. Therefore, all sides are 6in. So, we can substitute. We get

$P = 6\text{in} + 6\text{in} + 6\text{in} + 6\text{in}$

$P = 24\text{in}$

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Example Question #114 :Plane Geometry

Find the perimeter of a square with a length of 14cm.

Possible Answers:

$36\text{cm}$

$48\text{cm}$

$\text{There is not enough information to solve the problem.}$

$56\text{cm}$

$62\text{cm}$

Correct answer:

$56\text{cm}$

Explanation:

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

P = a+b+c+d

wherea, b, c,anddare the lengths of the sides of the square.

Now, we know the width of the square is 14cm. Because it is a square, all sides are equal. Therefore, all sides are 14cm. So, we get

$P = 14\text{cm} + 14\text{cm} + 14\text{cm} + 14\text{cm}$

$P = 56\text{cm}$

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Example Question #121 :Geometry

Find the perimeter of a square that has a length of 13in.

Possible Answers:

$169\text{in}$

$125\text{in}$

$39\text{in}$

$26\text{in}$

$52\text{in}$

Correct answer:

$52\text{in}$

Explanation:

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

P = a+b+c+d

wherea, b, c,anddare the lengths of the sides of the square.

Now, we know the length of the square is 13in. Because it is a square, all sides are equal. Therefore, all sides are 13in.

Knowing this, we can substitute into the formula. We get

$P = 13\text{in} +13\text{in} +13\text{in} +13\text{in}$

$P = 52\text{in}$

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

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

Possible Answers:

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

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

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

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

Correct answer:

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

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:

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

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

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

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

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

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

Square this to get the area:

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

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Example Question #3 :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 $\dpi{100} Area = side^{2}$ .

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

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

广场两边测量5meters. 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:

$9\ m^2$

$21\ m^2$

$49\ m^2$

$24\ m^{2}$

$8\ m^2$

Correct answer:

$24\ m^{2}$

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: $49-25=24\ m^2$

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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 $\frac{a}{b}$ . Give the ratio of the area of the second square to the area of the first square.

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

The area of a square can be found as follows:

Area=x^2

Where:

$x=Side\ Length$

So we can write:

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

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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 #111 :Plane Geometry

Example Question #112 :Plane Geometry

Example Question #113 :Plane Geometry

Example Question #114 :Plane Geometry

Example Question #121 :Geometry

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 #4 :How To Find The Area Of A Square

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

All ISEE Middle Level Math Resources

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