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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

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Example Questions

Example Question #701 : Ssat Upper Level Quantitative (Math)

The area of a right triangle is 100m^2 . If the base of the triangle is 25m , what is the height, in meters?

Possible Answers:

Correct answer:

Explanation:

To find the height, plug what is given in the question into the formula used to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Use the information given in the question:

$\text{Base}=25$

$\text{Area}=100$

$100=\frac{25\times height}{2}$

Now, solve for the height.

$25\times height=200$

height=8

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Example Question #37 : Properties Of Triangles

The area of a right triangle is 45m^2 , and the base is 15m . What is the height, in meters?

Possible Answers:

Correct answer:

Explanation:

To find the height, plug what is given in the question into the formula used to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Use the information given in the question:

$\text{Base}=15$

$\text{Area}=45$

$45=\frac{15\times height}{2}$

Now, solve for the height.

$15\times height=90$

height=6

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Example Question #38 : Properties Of Triangles

The area of a right triangle is $50\textup{ in}^2$ . If the base of the triangle is $10\textup{ in}$ , what is the length of the height, in inches?

Possible Answers:

Correct answer:

Explanation:

To find the height, plug what is given in the question into the formula used to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Use the information given in the question:

$\text{Base}=10$

$\text{Area}=50$

$50=\frac{10\times height}{2}$

Now, solve for the height.

$10\times height=100$

height=10

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

Right Triangle A has hypotenuse 25 inches and one leg of length 24 inches; Right Triangle B has hypotenuse 15 inches and one leg of length 9 inches; Rectangle C has length 16 inches. The area of Rectangle C is the sum of the areas of the two right triangles. What is the width of Rectangle C?

Possible Answers:

$17 \frac{1}{4} \textrm{ in}$

$6 \frac{7}{8} \textrm{ in}$

$10 \frac{1}{2} \textrm{ in}$

$8 \frac{5}{8} \textrm{ in}$

$14\frac{7}{8} \textrm{ in}$

Correct answer:

$8 \frac{5}{8} \textrm{ in}$

Explanation:

The area of a right triangle is half the product of its legs. In each case, we know the length of one leg and the hypotenuse, so we need to apply the Pythagorean Theorem to find the second leg, then take half the product of the legs:

Right Triangle A:

The length of the second leg is

$\sqrt{25^{2} -24 ^{2}} = \sqrt{625 - 576} = \sqrt{49} = 7$ inches.

The area is

$\frac{1}{2} \times 7 \times 24 = 84$ square inches.

Right Triangle B:

The length of the second leg is

$\sqrt{15^{2} -9 ^{2}} = \sqrt{225 - 81} = \sqrt{144} = 12$ inches.

The area is

$\frac{1}{2} \times 9 \times 12 = 54$ square inches.

The sum of the areas is 84 + 54 = 138 square inches.

The area of a rectangle is the product of its length and its height. Therefore, the height is the quotient of the area and the length, which, for Rectangle C, is $138 \div 16 = 8 \frac{5}{8}$ inches.

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Example Question #4 : Geometry

Right Triangle A has legs of lengths 10 inches and 14 inches; Right Triangle B has legs of length 20 inches and 13 inches; Rectangle C has length 30 inches. The area of Rectangle C is the sum of the areas of the two right triangles. What is the height of Rectangle C?

Possible Answers:

Insufficient information is given to determine the height.

$6 \frac{2}{3} \textrm{ in}$

$10 \textrm{ in}$

$13\frac{1}{3} \textrm{ in}$

$5 \textrm{ in}$

Correct answer:

$6 \frac{2}{3} \textrm{ in}$

Explanation:

The area of a right triangle is half the product of its legs. The area of Right Triangle A is equal to $\frac{1}{2} \times 10 \times 14 = 70$ square inches; that of Right Triangle B is equal to $\frac{1}{2} \times 20 \times 13 = 130$ square inches. The sum of the areas is 70 + 130 = 200 square inches, which is the area of Rectangle C.

The area of a rectangle is the product of its length and its height. Therefore, the height is the quotient of the area and the length, which, for Rectangle C, is $200 \div 30 = 6 \frac{2}{3}$ inches.

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

A right triangle has leg lengths of $10\text{ and }12$ . What is the area of this triangle?

Possible Answers:

120

Correct answer:

Explanation:

Since the legs of a right triangle form a right angle, you can use these as the base and the height of the triangle.

$\text{Area}=\frac{1}{2}(\text{base})(\text{height})$

$\text{Area}=\frac{1}{2}(10)(12)=\frac{1}{2}(120)=60$

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

A right triangle has leg lengths of $6\:cm$ and $9\:cm$ . Find the area of the right triangle.

Possible Answers:

$27\:cm^2$

$15\:cm^2$

$54\:cm^2$

$\frac{15}{2}\:cm^2$

Correct answer:

$27\:cm^2$

Explanation:

The legs of a right triangle also make up its base and its height.

$\text{Area}=\frac{1}{2}\text{base}\times\text{height}$

$\text{Area}=\frac{1}{2}\times6\:cm\times9\:cm=27\:cm^2$

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

A right triangle has leg lengths of $9\:cm$ and $12\:cm$ . Find the area of this triangle.

Possible Answers:

$54\:cm^2$

$15\:cm^2$

$108\:cm^2$

$15\sqrt2\:cm^2$

Correct answer:

$54\:cm^2$

Explanation:

The legs of a right triangle are also its height and its base.

$\text{Area}=\frac{1}{2}\text{base}\times\text{height}$

$\text{Area}=\frac{1}{2}(9\:cm)(12\:cm)=54\:cm^2$

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

A right triangle has two legs of lengths $9\:cm$ and $12\:cm$ , respectively. What is the area of the right triangle?

Possible Answers:

$108\:cm^{2}$

$54\:cm^{2}$

$72\:cm^{2}$

$36\:cm^2$

$124\:cm^2$

Correct answer:

$54\:cm^{2}$

Explanation:

The area of a right triangle with a base and a height can be found with the formula $A=\frac{1}{2}bh$ . Since the two legs of a right triangle are perpendicular to each other, we can use these as the base and height in the formula. Therefore:

$A=\frac{1}{2}(9\:cm)(12\:cm)$

$A=\frac{1}{2}(108\:cm^{2})$

$A=54\:cm^{2}$

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Example Question #44 : Properties Of Triangles

A given right triangle has two legs of lengths $6\:cm$ and $8\:cm$ , respectively. What is the area of the triangle?

Possible Answers:

$7\:cm^2$

Not enough information to solve

$48\:cm^2$

$24\:cm^2$

$14\:cm^2$

Correct answer:

$24\:cm^2$

Explanation:

$A=\frac{1}{2}bh$

$A=\frac{1}{2}(6\:cm)(8\:cm)$

$A=\frac{1}{2}(48\:cm^2)$

$A=24\:cm^2$

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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #701 : Ssat Upper Level Quantitative (Math)

Example Question #37 : Properties Of Triangles

Example Question #38 : Properties Of Triangles

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

Example Question #4 : Geometry

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

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

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

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

Example Question #44 : Properties Of Triangles

All SSAT Upper Level Math Resources

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