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SSAT Middle Level Math : Geometry

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Example Questions

Example Question #244 : Ssat Middle Level Quantitative (Math)

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 #245 : Ssat Middle Level Quantitative (Math)

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:

4,4,11

5,5,8

4,5,9

5,6,7

5,5,7

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 #1 : 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

2 feet 10 inches

3 feet 2 inches

2 feet 2 inches

2 feet 6 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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Example Question #23 : Triangles

Find the perimeter of the triangle above.

Note: Figure not drawn to scale.

Possible Answers:

None of these answers are correct.

$24\: in$

$72\: in$

$20\: in$

$32\: in$

Correct answer:

$24\: in$

Explanation:

The perimeter of a shape is the length around the shape. In order to find the perimeter of a triangle, add the lengths of the sides: 8+12+4=24 .

Because the lengths are in inches, the answer must be in inches as well.

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

If the triangle below is an isosceles triangle, what of the following choices could be its perimeter?

Possible Answers:

Correct answer:

Explanation:

An isosceles triangle has 2 equal sides and a third side that is unequal. If one given side is 5 and the other is 7, then the third missing side must equal either 5 or 7. If the missing side has length 5, then the perimeter is 17 (5+5+7). If the missing side is of length 7, then the perimeter is 19 (7+7+5). Of the two, only 19 is an answer choice, so the correct answer is 19.

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Example Question #24 : Triangles

The perimeter of equilateral triangle QRS is 4 times the perimeter of equilateral triangle TUV. If the perimeter of QRS is 36, what is the length of one side of TUV?

Possible Answers:

Correct answer:

Explanation:

If the perimeter of QRS is 4 times the perimeter of TUV, and the perimeter of QRS is 36, then the perimeter of TUV is equal to 36 divided by 4, which is 9. If the perimeter of equilateral triangle TUV is 9, then each individual side must have length 3.

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Example Question #25 : Triangles

What is the perimeter, in feet, of an equilateral triangle that has a side of 36 inches?

Possible Answers:

$21\ \text{ft}$

$12\ \text{ft}$

$9\ \text{ft}$

$36\ \text{ft}$

$14\ \text{ft}$

Correct answer:

$9\ \text{ft}$

Explanation:

Given that there are 12 inches in a foot, 36 inches is equal to 3 feet because 36 divided by 12 equals 3.

$36\ \text{in}\div 12\ \text{in per ft}=3\ \text{ft}$

In an equilateral triangle, each side is equal. Thus, if one side is 3 feet long, that means that each of the other two sides are also 3 feet long.

Add the sides together to find the total perimeter.

P=s+s+s=3s

s=3

P=3+3+3=9

The perimeter of the triangle is 9 feet.

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Example Question #26 : Triangles

The perimeter of an isosceles triangle is 19. What is the possible list of the lengths of the sides?

Possible Answers:

(6, 6, 7)

(5, 4, 10)

(5, 6, 8)

(2, 8, 9)

(11, 6, 2)

Correct answer:

(6, 6, 7)

Explanation:

Since the triangle is an isoscles, two of the sides must be equal. They must also add to . Looking at the possibilities, only (6, 6, 7) have two sides that are the same length. Now we need to check the triangle inequality to make sure the lengths create a triangle. The triangle inequality is:

A+B>C

A+C>B

B+C>A

Plugging (6, 6, 7) into these inequalities we get:

6+6>7

6+7>6

Therefore, the inequalities hold true thus, (6, 6, 7) creates a triangle. Now we need to look at the sum of the lengths:

6+6+7=19

Therefore, (6, 6, 7) is the correct answer.

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SSAT Middle Level Math : Geometry

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #244 : Ssat Middle Level Quantitative (Math)

Example Question #17 : Plane Geometry

Example Question #245 : Ssat Middle Level Quantitative (Math)

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

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

Example Question #23 : Triangles

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

Example Question #24 : Triangles

Example Question #25 : Triangles

Example Question #26 : Triangles

All SSAT Middle Level Math Resources

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