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ISEE Middle Level Math : Quadrilaterals

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Example Questions

Example Question #51 : Squares

Use the following square to answer the question:

Square2

Find the area.

Possible Answers:

$28\text{cm}^2$ $\displaystyle 28\text{cm}^2$

$108\text{cm}^2$ $\displaystyle 108\text{cm}^2$

$196\text{cm}^2$ $\displaystyle 196\text{cm}^2$

$56\text{cm}^2$ $\displaystyle 56\text{cm}^2$

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

Correct answer:

$196\text{cm}^2$ $\displaystyle 196\text{cm}^2$

Explanation:

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

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

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

$\text{area of square} = 14\text{cm} \cdot 14\text{cm}$ $\displaystyle \text{area of square} = 14\text{cm} \cdot 14\text{cm}$

$\text{area of square} = 196\text{cm}^2$ $\displaystyle \text{area of square} = 196\text{cm}^2$

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Example Question #51 : Quadrilaterals

Find the area of a square with a length of 8in.

Possible Answers:

$32\text{in}^2$ $\displaystyle 32\text{in}^2$

$24\text{in}^2$ $\displaystyle 24\text{in}^2$

$56\text{in}^2$ $\displaystyle 56\text{in}^2$

$64\text{in}^2$ $\displaystyle 64\text{in}^2$

$72\text{in}^2$ $\displaystyle 72\text{in}^2$

Correct answer:

$64\text{in}^2$ $\displaystyle 64\text{in}^2$

Explanation:

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

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

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

So, we know the length of the square is 8in. Because it is a square, all sides are equal. Therefore, the width is also 8in.

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

$\text{area of square} = 8\text{in} \cdot 8\text{in}$ $\displaystyle \text{area of square} = 8\text{in} \cdot 8\text{in}$

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

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Example Question #51 : Quadrilaterals

Find the area of a square that has a width of 15in.

Possible Answers:

$225\text{in}^2$ $\displaystyle 225\text{in}^2$

$60\text{in}^2$ $\displaystyle 60\text{in}^2$

$125\text{in}^2$ $\displaystyle 125\text{in}^2$

$45\text{in}^2$ $\displaystyle 45\text{in}^2$

$30\text{in}^2$ $\displaystyle 30\text{in}^2$

Correct answer:

$225\text{in}^2$ $\displaystyle 225\text{in}^2$

Explanation:

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

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

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

Now, we know the width of the square is 15in. Because it is a square, all sides are equal. Therefore, the length is also 15in.

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

$\text{area of square} = 15\text{in} \cdot 15\text{in}$ $\displaystyle \text{area of square} = 15\text{in} \cdot 15\text{in}$

$\text{area of square} = 225\text{in}^2$ $\displaystyle \text{area of square} = 225\text{in}^2$

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Example Question #52 : Quadrilaterals

Find the area of a square with a base of 18cm.

Possible Answers:

$124\text{cm}^2$ $\displaystyle 124\text{cm}^2$

$36\text{cm}^2$ $\displaystyle 36\text{cm}^2$

$324\text{cm}^2$ $\displaystyle 324\text{cm}^2$

$248\text{cm}^2$ $\displaystyle 248\text{cm}^2$

$72\text{cm}^2$ $\displaystyle 72\text{cm}^2$

Correct answer:

$324\text{cm}^2$ $\displaystyle 324\text{cm}^2$

Explanation:

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

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

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

Now, we know the base of the square is 18cm. Because it is a square, all sides are equal. Therefore, the length is also 18cm.

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

$\text{area of square} = 18\text{cm} \cdot 18\text{cm}$ $\displaystyle \text{area of square} = 18\text{cm} \cdot 18\text{cm}$

$\text{area of square} = 324\text{cm}^2$ $\displaystyle \text{area of square} = 324\text{cm}^2$

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Example Question #53 : Quadrilaterals

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

Possible Answers:

$169\text{in}^2$ $\displaystyle 169\text{in}^2$

$121\text{in}^2$ $\displaystyle 121\text{in}^2$

$100\text{in}^2$ $\displaystyle 100\text{in}^2$

$144\text{in}^2$ $\displaystyle 144\text{in}^2$

$172\text{in}^2$ $\displaystyle 172\text{in}^2$

Correct answer:

$169\text{in}^2$ $\displaystyle 169\text{in}^2$

Explanation:

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

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

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

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

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

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Example Question #151 : Plane Geometry

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

Possible Answers:

$289\text{cm}^2$ $\displaystyle 289\text{cm}^2$

$312\text{cm}^2$ $\displaystyle 312\text{cm}^2$

$68\text{cm}^2$ $\displaystyle 68\text{cm}^2$

$178\text{cm}^2$ $\displaystyle 178\text{cm}^2$

$204\text{cm}^2$ $\displaystyle 204\text{cm}^2$

Correct answer:

$289\text{cm}^2$ $\displaystyle 289\text{cm}^2$

Explanation:

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

$A = l \cdot w$ $\displaystyle A = l \cdot w$

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

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

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

Report an Error

Example Question #31 : How To Find The Area Of A Square

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

Possible Answers:

$76\text{cm}^2$ $\displaystyle 76\text{cm}^2$

$121\text{cm}^2$ $\displaystyle 121\text{cm}^2$

$96\text{cm}^2$ $\displaystyle 96\text{cm}^2$

$256\text{cm}^2$ $\displaystyle 256\text{cm}^2$

$361\text{cm}^2$ $\displaystyle 361\text{cm}^2$

Correct answer:

$361\text{cm}^2$ $\displaystyle 361\text{cm}^2$

Explanation:

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

$A = l \cdot w$ $\displaystyle A = l \cdot w$

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

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

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

Report an Error

Example Question #53 : Squares

Use the following square to answer the question:

Square2

Find the area.

Possible Answers:

$169\text{cm}^2$ $\displaystyle 169\text{cm}^2$

$196\text{cm}^2$ $\displaystyle 196\text{cm}^2$

$144\text{cm}^2$ $\displaystyle 144\text{cm}^2$

$56\text{cm}^2$ $\displaystyle 56\text{cm}^2$

$72\text{cm}^2$ $\displaystyle 72\text{cm}^2$

Correct answer:

$196\text{cm}^2$ $\displaystyle 196\text{cm}^2$

Explanation:

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

$A = l \cdot w$ $\displaystyle A = l \cdot w$

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

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

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

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Example Question #54 : Squares

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

Possible Answers:

$13\text{in}$ $\displaystyle 13\text{in}$

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

$22\text{in}$ $\displaystyle 22\text{in}$

$12\text{in}$ $\displaystyle 12\text{in}$

$11\text{in}$ $\displaystyle 11\text{in}$

Correct answer:

$11\text{in}$ $\displaystyle 11\text{in}$

Explanation:

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

A = x^2 $\displaystyle A = x^2$

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 $121\text{in}^2$ $\displaystyle 121\text{in}^2$. So, we will substitute.

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

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

$11\text{in} = x$ $\displaystyle 11\text{in} = x$

$x = 11\text{in}$ $\displaystyle x = 11\text{in}$

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

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Example Question #52 : Squares

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

Possible Answers:

$136\text{in}^2$ $\displaystyle 136\text{in}^2$

$144\text{in}^2$ $\displaystyle 144\text{in}^2$

$121\text{in}^2$ $\displaystyle 121\text{in}^2$

$96\text{in}^2$ $\displaystyle 96\text{in}^2$

$48\text{in}^2$ $\displaystyle 48\text{in}^2$

Correct answer:

$144\text{in}^2$ $\displaystyle 144\text{in}^2$

Explanation:

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

$A = l \cdot w$ $\displaystyle A = l \cdot w$

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.

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

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

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : Quadrilaterals

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #51 : Squares

Example Question #51 : Quadrilaterals

Example Question #51 : Quadrilaterals

Example Question #52 : Quadrilaterals

Example Question #53 : Quadrilaterals

Example Question #151 : Plane Geometry

Example Question #31 : How To Find The Area Of A Square

Example Question #53 : Squares

Example Question #54 : Squares

Example Question #52 : Squares

All ISEE Middle Level Math Resources

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