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ISEE Middle Level Math : Plane Geometry

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Example Questions

Example Question #151 : Plane Geometry

Find the area of a square with a width of 13in.

Possible Answers:

$172\text{in}^2$

$169\text{in}^2$

$144\text{in}^2$

$121\text{in}^2$

$100\text{in}^2$

Correct answer:

$169\text{in}^2$

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

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

$\text{area of square} = 13\text{in} \cdot 13\text{in}$

$\text{area of square} = 169\text{in}^2$

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Example Question #151 : Plane Geometry

Find the area of a square with a base of 17cm.

Possible Answers:

$289\text{cm}^2$

$312\text{cm}^2$

$68\text{cm}^2$

$178\text{cm}^2$

$204\text{cm}^2$

Correct answer:

$289\text{cm}^2$

Explanation:

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

$A = l \cdot w$

Now, we know the length of the square is 17cm. Because it is a square, all sides are equal. Therefore, the width is also 17cm.

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

$A = 17\text{cm} \cdot 17\text{cm}$

$A = 289\text{cm}^2$

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Example Question #52 : Squares

Find the area of a square with a base of 19cm.

Possible Answers:

$361\text{cm}^2$

$96\text{cm}^2$

$76\text{cm}^2$

$121\text{cm}^2$

$256\text{cm}^2$

Correct answer:

$361\text{cm}^2$

Explanation:

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

$A = l \cdot w$

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

Now, we know the base (or length) of the square is 19cm. Because it is a square, all sides are equal. Therefore, the width is also 19cm.

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

$A = 19\text{cm} \cdot 19\text{cm}$

$A = 361\text{cm}^2$

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Example Question #53 : Squares

Use the following square to answer the question:

Square2

Find the area.

Possible Answers:

$169\text{cm}^2$

$196\text{cm}^2$

$144\text{cm}^2$

$56\text{cm}^2$

$72\text{cm}^2$

Correct answer:

$196\text{cm}^2$

Explanation:

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

$A = l \cdot w$

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

Now, given the square

Square2

we can see the length is 14cm. Because it is a square, all sides are equal. Therefore, the width is also 14cm. Knowing this, we can substitute into the formula. We get

$A = 14\text{cm} \cdot 14\text{cm}$

$A = 196\text{cm}^2$

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Example Question #54 : Squares

The area of a square is $121\text{in}^2$ . Find the length of one side of the square.

Possible Answers:

$13\text{in}$

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

$22\text{in}$

$12\text{in}$

$11\text{in}$

Correct answer:

$11\text{in}$

Explanation:

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

A = x^2

where x is the length of one side.

Now, we want to find the length of one side, so we will solve for x. We know the area of the square is $121\text{in}^2$ . So, we will substitute.

$121\text{in}^2 = x^2$

$\sqrt{121\text{in}^2} = \sqrt{x^2}$

$11\text{in} = x$

$x = 11\text{in}$

Therefore, the length of one side of the square is 11in.

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Example Question #151 : Geometry

Find the area of a square with a length of 12in.

Possible Answers:

$96\text{in}^2$

$136\text{in}^2$

$144\text{in}^2$

$121\text{in}^2$

$48\text{in}^2$

Correct answer:

$144\text{in}^2$

Explanation:

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

$A = l \cdot w$

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

Now, we know the length of the square is 12in. Because it is a square, all sides are equal. Therefore, the width is also 12in. So, we can substitute.

$A = 12\text{in} \cdot 12\text{in}$

$A = 144\text{in}^2$

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Example Question #152 : Plane Geometry

Find the area of a square with a width of 5in.

Possible Answers:

$15\text{in}^2$

$25\text{in}^2$

$30\text{in}^2$

$20\text{in}^2$

$10\text{in}^2$

Correct answer:

$25\text{in}^2$

Explanation:

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

$A = l \cdot w$

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

Now, we know the width of the square is 5in. Because it is a square, all sides are equal. Therefore, the length is also 5in. So, we can substitute. We get

$A = 5\text{in} \cdot 5\text{in}$

$A = 25\text{in}^2$

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Example Question #153 : Plane Geometry

Find the area of a square with a length of 9in.

Possible Answers:

$63\text{in}^2$

$72\text{in}^2$

$45\text{in}^2$

$36\text{in}^2$

$81\text{in}^2$

Correct answer:

$81\text{in}^2$

Explanation:

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

$A = l \cdot w$

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

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

$A = 9\text{in} \cdot 9\text{in}$

$A = 81\text{in}^2$

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Example Question #61 : Quadrilaterals

Find the area of a square that has a width of 13in.

Possible Answers:

$52\text{in}^2$

$39\text{in}^2$

$26\text{in}^2$

$169\text{in}^2$

$118\text{in}^2$

Correct answer:

$169\text{in}^2$

Explanation:

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

$A = l \cdot w$

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

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

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

$A = 13\text{in} \cdot 13\text{in}$

$A = 169\text{in}^2$

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

What is the area of a rectangle with length $14\ cm$ and width $12\ cm$ ?

Possible Answers:

$144\; cm^{2}$

$158\;cm^{2}$

$168\;cm^{2}$

$148\; cm^{2}$

$198\;cm^{2}$

Correct answer:

$168\;cm^{2}$

Explanation:

The formula for the area, , of a rectangle when we are given its length, , and width, , is A = L * W .

To calculate this area, just multiply the two terms.

$A = 14\ cm * 12\ cm = 168\; cm^{2}$

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : Plane Geometry

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #151 : Plane Geometry

Example Question #151 : Plane Geometry

Example Question #52 : Squares

Example Question #53 : Squares

Example Question #54 : Squares

Example Question #151 : Geometry

Example Question #152 : Plane Geometry

Example Question #153 : Plane Geometry

Example Question #61 : Quadrilaterals

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

All ISEE Middle Level Math Resources

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