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SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)

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

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All SSAT Middle Level Math Resources

10 Diagnostic Tests 225 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #4 : Area Of A Triangle

A triangle has a height of 9 inches and a base that is one third as long as the height. What is the area of the triangle, in square inches?

Possible Answers:

$\frac{27}{2}$

None of these

Correct answer:

$\frac{27}{2}$

Explanation:

The area of a triangle is found by multiplying the base times the height, divided by 2.

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

Given that the height is 9 inches, and the base is one third of the height, the base will be 3 inches.

$b=h\div3=9\div3=3$

We now have both the base (3) and height (9) of the triangle. We can use the equation to solve for the area.

$\text{Area} =\frac{9\times 3}{2}$

$\text{Area} =\frac{27}{2}$

The fraction cannot be simplified.

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Example Question #51 : Geometry

The hypotenuse of a right triangle is feet; it has one leg feet long. Give its area in square inches.

Possible Answers:

$101,088 \textrm{ in}^{2}$

$77,760 \textrm{ in}^{2}$

$38,880 \textrm{ in}^{2}$

$43,120 \textrm{ in}^{2}$

$42,120 \textrm{ in}^{2}$

Correct answer:

$38,880 \textrm{ in}^{2}$

Explanation:

The area of a right triangle is half the product of the lengths of its legs, so we need to use the Pythagorean Theorem to find the length of the other leg. Set c = 39 , b = 36 :

$a^{2} = c^{2} - b^{2}$

$a^{2} = 39 ^{2} - 36^{2}$

$a^{2} = 1,521 - 1,296$

$a^{2} = 225$

$a = \sqrt{225} = 15$

The legs have length and feet; multiply both dimensions by to convert to inches:

$15 \times 12 = 180$ inches

$36 \times 12 = 432$ inches.

Now find half the product:

$A = \frac{1}{2} \cdot 180 \cdot 432 = 38,880\ in^{2}$

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Example Question #101 : Geometry

What is the area (in square feet) of a triangle with a base of feet and a height of feet?

Possible Answers:

Correct answer:

Explanation:

The area of a triangle is found by multiplying the base times the height, divided by .

$Area =\frac{base\cdot height}{2}$

$Area =\frac{4\cdot 7}{2}$

Area=14

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Example Question #11 : Triangles

What is the area of a triangle with a base of and a height of ?

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a triangle is $\dpi{100} Area=\frac{1}{2}\times base\times height$ .

Plug the given values into the formula to solve:

$\dpi{100} Area=\frac{1}{2}\times 12\times 3$

$\dpi{100} Area=\frac{1}{2}\times 36$

$\dpi{100} Area=18$

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Example Question #15 : How To Find The Area Of A Triangle

Right triangle 2

Give the perimeter of the above triangle in feet.

Possible Answers:

$2 \frac{2}{3}\textrm{ ft }$

$3 \frac{1}{3}\textrm{ ft }$

$3 \frac{1}{2}\textrm{ ft }$

$2 \frac{1}{2}\textrm{ ft }$

Correct answer:

$2 \frac{1}{2}\textrm{ ft }$

Explanation:

The perimeter of the triangle - the sum of the lengths of its sides - is

5 + 12 + 13 = 30 inches.

Divide by 12 to convert to feet:

$30 \div 12 = 2 \textrm{ R }6$

As a fraction, this is $2 \frac{6}{12}$ or $2 \frac{1}{2}$ feet,

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Example Question #11 : Plane Geometry

Rectangles 3

The above diagram shows Rectangle RECT , with midpoint of $\overline{CT}$ .

The area of $\bigtriangleup ECM$ is 225. Evaluate

Possible Answers:

Correct answer:

Explanation:

is the midpoint of $\overline{CT}$ , so $\bigtriangleup ECM$ has as its base $CM= \frac{1}{2} \cdot CT = \frac{1}{2} \cdot 2x =x$ ; its height is $EC = \frac{1}{2} x$ .

Its area is half their product, or

$\frac{1}{2} \cdot x \cdot \frac{1}{2} x = \frac{1}{4} x^{2}$

Set this equal to 225:

$\frac{1}{4} x^{2} = 225$

$4 \cdot \frac{1}{4} x^{2} = 4 \cdot 225$

$x^{2} = 900$

$x = \sqrt{900}= 30$ .

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Example Question #17 : Plane Geometry

Find the area of a triangle with a height of 12in and a base that is half the height.

Possible Answers:

$30\text{in}^2$

$6\text{in}^2$

$18\text{in}^2$

$24\text{in}^2$

$36\text{in}^2$

Correct answer:

$36\text{in}^2$

Explanation:

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

$A = \frac{1}{2} \cdot b \cdot h$

where b is the base and h is the height of the triangle.

Now, we know the height of the triangle is 12in. We also know the base of the triangle is half of the height. Therefore, the base of the triangle is 6in.

So, we can substitute. We get

$A = \frac{1}{2} \cdot 6\text{in} \cdot 12\text{in}$

$A = 3\text{in} \cdot 12\text{in}$

$A = 36\text{in}^2$

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Example Question #21 : Plane Geometry

Find the area of the triangle below

Screen shot 2015 11 10 at 9.45.10 pm

Possible Answers:

$21 \frac{1}{3}$

Correct answer:

Explanation:

The equation for area of a triangle is

$\frac{b\times h}{2}$ .

In this case the coordinates of the base are (-3,0)(5,0) , which means the length of the base is 5--3=8 .

The coordinates of the side that determines the height are (-3,0)(-3,8) .

Therefore the height is 8-0=8 .

$\frac{8\times8}{2}=\frac{64}{2}=32$ .

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Example Question #1 : How To Find Perimeter Of A Triangle

The perimeter of an isosceles triangle is 18. What is a possible list of the lengths of the sides?

Possible Answers:

5,5,7

5,6,7

4,5,9

5,5,8

4,4,11

Correct answer:

5,5,8

Explanation:

Since it is isosceles, 2 of the sides must be equal. They must also add to 18.

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Example Question #2 : How To Find Perimeter Of A Triangle

An equilateral triangle has perimeter 8 feet 6 inches. How long is one side?

Possible Answers:

3 feet 4 inches

3 feet 2 inches

2 feet 2 inches

2 feet 6 inches

2 feet 10 inches

Correct answer:

2 feet 10 inches

Explanation:

One foot is equal to 12 inches, so the perimeter 8 feet 6 inches is equal to $8 \times 12 + 6 = 96 + 6 = 102$ inches.

An equilateral triangle has three sides of equal measure, so divide its perimeter by 3:

$102 \div 3 = 34$

To convert 34 inches to feet and inches:

$34\div 12 = 2 \textrm{ R }10$

One side measures 2 feet 10 inches.

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SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #4 : Area Of A Triangle

Example Question #51 : Geometry

Example Question #101 : Geometry

Example Question #11 : Triangles

Example Question #15 : How To Find The Area Of A Triangle

Example Question #11 : Plane Geometry

Example Question #17 : Plane Geometry

Example Question #21 : Plane Geometry

Example Question #1 : How To Find Perimeter Of A Triangle

Example Question #2 : How To Find Perimeter Of A Triangle

All SSAT Middle Level Math Resources

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