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HSPT Math : Geometry

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6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : How To Find The Perimeter Of A Figure

A circle has radius 8. The circumference of the circle is 40% of what number?

Possible Answers:

$80 \pi$

$40 \pi$

$2 0 \pi$

$25 \pi$

Correct answer:

$40 \pi$

Explanation:

The circumference of a circle is its radius mulitplied by $2 \pi$ . The radius is 8, so the circumference is

$8 \cdot 2 \pi = 16 \pi$ .

To find the number of which this is 40%, divide this by 40%, or $\frac{40 }{100}$ :

$16 \pi \div\frac{40 }{100} = 16 \pi \div\frac{2}{5} = 16 \pi \cdot \frac{5} {2} = \frac{80 \pi} {2} = 40 \pi$

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Example Question #12 : How To Find The Perimeter Of A Figure

$\bigtriangleup ABC \sim \bigtriangleup DEF$ .

$\angle B$ is a right angle.

$m \angle C = 45 ^{\circ }$ .

Is $\bigtriangleup DEF$ scalene, isosceles, or equilateral - or can it be determined?

Possible Answers:

Whether $\bigtriangleup DEF$ is scalene, isosceles, or equilateral cannot be determined.

$\bigtriangleup DEF$ is an equilateral triangle.

$\bigtriangleup DEF$ is a isosceles triangle, but not equilateral.

$\bigtriangleup DEF$ is a scalene triangle.

Correct answer:

$\bigtriangleup DEF$ is a isosceles triangle, but not equilateral.

Explanation:

Corresponding angles of similar triangles are congruent, so

$m \angle E = m \angle B = 90 ^{\circ }$

$m \angle F = m \angle C = 45 ^{\circ }$

The degree measures of the angles of a triangle total 180, so

$m \angle D =180^{\circ } - (m \angle F +m \angle E )$

$m \angle D =180^{\circ } - (90^{\circ } +45^{\circ } ) = 45^{\circ }$

Since $\angle D$ and $\angle F$ are congruent, by the Isosceles Triangle Theorem,

$\overline{EF} \cong \overline{DE}$

making $\bigtriangleup DEF$ isosceles.

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Example Question #263 : Problem Solving

A ladder 30 feet long leans against a house. The top of the ladder is feet above the ground. In terms of , how far along the ground is the bottom of the ladder from the house?

Possible Answers:

30 + N

$\sqrt{900 + N^{2}}$

$\sqrt{900 - N^{2}}$

30 - N

Correct answer:

$\sqrt{900 - N^{2}}$

Explanation:

The ladder, which is 30 feet long, is the hypotenuse of a right triangle whose legs are the line from the top of the ladder to the ground, which has length feet, and the line from the bottom of the ladder horizontally to the house, whose length we will call feet. See the diagram below.

Ladder

By the Pythagorean Theorem,

$M^{2}+N^{2} = 30 ^{2} = 900$

Solving for :

$M^{2}+N^{2} - N^{2} = 900 - N^{2}$

$M^{2}= 900 - N^{2}$

$M = \sqrt{900 - N^{2}}$ , the correct choice.

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Example Question #6 : Parallelograms

What is the perimeter of the polygon below?

Possible Answers:

48in

45in

46in

47in

43in

Correct answer:

48in

Explanation:

To find the area of a perimeter, we add all of the side lengths together.

9+15+6+8+3+7=48

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Example Question #7 : Parallelograms

What is the perimeter of the polygon below?

Possible Answers:

32in

31in

33in

38in

30in

Correct answer:

32in

Explanation:

To find the area of a perimeter, we add all of the side lengths together.

8+7+4+1+4+8=32

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Example Question #8 : Parallelograms

What is the perimeter of the polygon below?

Possible Answers:

42in

40in

44in

43in

41in

Correct answer:

42in

Explanation:

To find the area of a perimeter, we add all of the side lengths together.

12+5+8+4+4+9=42

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Example Question #21 : Plane Geometry

What is the perimeter of the polygon below?

Possible Answers:

54in

53in

52in

55in

51in

Correct answer:

52in

Explanation:

To find the area of a perimeter, we add all of the side lengths together.

15+10+5+1+10+11=52

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Example Question #22 : Plane Geometry

What is the perimeter of the polygon below?

Possible Answers:

42in

41in

44in

40in

43in

Correct answer:

40in

Explanation:

To find the area of a perimeter, we add all of the side lengths together.

8+12+4+6+4+6=40

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Example Question #1871 : Common Core Math: Grade 3

What is the perimeter of the polygon below?

Possible Answers:

38in

35in

36in

37in

34in

Correct answer:

38in

Explanation:

To find the area of a perimeter, we add all of the side lengths together.

7+7+2+5+5+12=38

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Example Question #511 : Measurement & Data

What is the perimeter of the polygon below?

Possible Answers:

43in

47in

44in

45in

46in

Correct answer:

46in

Explanation:

To find the area of a perimeter, we add all of the side lengths together.

4+12+11+6+7+6=46

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HSPT Math : Geometry

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #11 : How To Find The Perimeter Of A Figure

Example Question #12 : How To Find The Perimeter Of A Figure

Example Question #263 : Problem Solving

Example Question #6 : Parallelograms

Example Question #7 : Parallelograms

Example Question #8 : Parallelograms

Example Question #21 : Plane Geometry

Example Question #22 : Plane Geometry

Example Question #1871 : Common Core Math: Grade 3

Example Question #511 : Measurement & Data

All HSPT Math Resources

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