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SSAT Upper Level Math : Geometry

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

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All SSAT Upper Level Math Resources

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Example Questions

Example Question #541 : Geometry

Find the perimeter of a triangle with side lengths $45, 40,\text{ and }35$ .

Possible Answers:

110

120

130

115

Correct answer:

120

Explanation:

To find the perimeter of a triangle, add up all of its sides.

$\text{Perimeter}=45+35+40=120$

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Example Question #542 : Geometry

Bill has a triangular garden that he needs to fence. The garden has side lengths of $\text{9 feet, 10 feet, and 12 feet}$ . In feet, how much fencing will Bill need?

Possible Answers:

36ft

31ft

35ft

22ft

Correct answer:

31ft

Explanation:

To find how much fencing Bill needs, you will need to find the perimeter of the triangle. The perimeter of a triangle is found by adding up all the sides together.

$\text{Perimeter}=9+10+12=31$

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Example Question #11 : Acute / Obtuse Triangles

Find the perimeter of a triangle with side lengths of 12, 12, 18 .

Possible Answers:

Correct answer:

Explanation:

To find the perimeter of a triangle, add up all of its sides.

$\text{Perimeter}=12+12+18=42$

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Example Question #12 : Acute / Obtuse Triangles

Find the perimeter of the triangle below:

Possible Answers:

Correct answer:

Explanation:

First, find the length of the missing side.

Since the angle measurements in the base of the triangle are the same, this is an isosceles triangle. The side lengths directly across from the equal angles must be the same. Thus, the missing side length is .

Now, to find the perimeter, add up all the side lengths.

$\text{Perimeter}=5+5+3=13$

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Example Question #13 : Acute / Obtuse Triangles

Find the perimeter of the triangle below:

Possible Answers:

Correct answer:

Explanation:

First, find the length of the missing side.

Now, to find the perimeter, add up all the side lengths.

$\text{Perimeter}=16+16+18=50$

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Example Question #14 : Acute / Obtuse Triangles

Find the perimeter of the triangle below:

Possible Answers:

Correct answer:

Explanation:

First, find the length of the missing side.

Since there are two angles that are the same, this is an isosceles triangle. The side lengths directly across from the equal angles must be the same. Thus, the missing side length is .

Now, to find the perimeter, add up all the side lengths.

$\text{Perimeter}=18+18+21=57$

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Example Question #15 : Acute / Obtuse Triangles

Find the perimeter of the triangle below:

Possible Answers:

Correct answer:

Explanation:

First, find the length of the missing side.

Since there are two angles that are the same, this is an isosceles triangle. The side lengths directly across from the equal angles must be the same. Thus, the missing side length is .

Now, to find the perimeter, add up all the side lengths.

$\text{Perimeter}=14+14+20=48$

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Example Question #16 : Acute / Obtuse Triangles

Triangle_a

Figure NOT drawn to scale.

If $x = 72^{\circ }$ and $y = 43^{\circ }$ , evaluate .

Possible Answers:

$137^{\circ}$

$108^{\circ}$

$115^{\circ }$

$125^{\circ }$

$65^{\circ}$

Correct answer:

$115^{\circ }$

Explanation:

The measure of an exterior angle of a triangle is the sum of the measures of its remote interior angles, so

$w = x + y = 72 + 43 = 115 ^{\circ }$

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Example Question #17 : Acute / Obtuse Triangles

If the vertex angle of an isoceles triangle is $64^{\circ}$ , what is the value of one of its base angles?

Possible Answers:

$36^{\circ}$

$58^{\circ}$

$116^{\circ}$

$26^{\circ}$

$64^{\circ}$

Correct answer:

$58^{\circ}$

Explanation:

In an isosceles triangle, the base angles are the same. Also, the three angles of a triangle add up to $180^{\circ}$ .

So, subtract the vertex angle from $180^{\circ}$ . You get $116^{\circ}$ .

Because there are two base angles you divide $116^{\circ}$ by , and you get $58^{\circ}$ .

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Example Question #2003 : Hspt Mathematics

Triangle

Note: Figure NOT drawn to scale.

Refer to the above diagram.

$45^{\circ } \leq m \angle 1 \leq 50^{\circ }$

$60^{\circ } \leq m \angle 2 \leq 70 ^{\circ }$

Which of the following could be a measure of $\angle 3$ ?

Possible Answers:

All of the other choices give a possible measure of $\angle 3$ .

$125^{\circ }$

$110^{\circ }$

$100^{\circ }$

$130^{\circ }$

Correct answer:

$110^{\circ }$

Explanation:

The measure of an exterior angle of a triangle is the sum of the measures of its remote interior angles, so

$\angle 3 = \angle 1 + \angle 2$ .

We also have the following constraints:

$45^{\circ } \leq m \angle 1 \leq 50^{\circ }$

$60^{\circ } \leq m \angle 2 \leq 70 ^{\circ }$

Then, by the addition property of inequalities,

$45^{\circ } + 60 ^{\circ }\leq m \angle 1 +m \angle 2 \leq 50^{\circ } + 70 ^{\circ }$

$105 ^{\circ }\leq m \angle 3 \leq 120^{\circ }$

Therefore, the measure of $\angle 3$ must fall in that range. Of the given choices, only $110^{\circ }$ falls in that range.

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Geometry

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #541 : Geometry

Example Question #542 : Geometry

Example Question #11 : Acute / Obtuse Triangles

Example Question #12 : Acute / Obtuse Triangles

Example Question #13 : Acute / Obtuse Triangles

Example Question #14 : Acute / Obtuse Triangles

Example Question #15 : Acute / Obtuse Triangles

Example Question #16 : Acute / Obtuse Triangles

Example Question #17 : Acute / Obtuse Triangles

Example Question #2003 : Hspt Mathematics

All SSAT Upper Level Math Resources

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