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HSPT Math : How to find the perimeter of a figure

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Example Questions

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Example Question #261 : Problem Solving

What is the perimeter of a square with a side length of a-1 ?

Possible Answers:

a-4

a^2-4

4a^2-4

4a-4

4a+4

Correct answer:

4a-4

Explanation:

Write the perimeter formula for a square.

P=4s

Substitute the side length in the formula and simplify.

P=4(a-1)= 4a-4

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Example Question #263 : Problem Solving

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

Possible Answers:

$25 \pi$

$2 0 \pi$

$80 \pi$

$40 \pi$

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 #62 : Geometry

$\bigtriangleup ABC \sim \bigtriangleup DEF$ .

$\angle B$ is a right angle.

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

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

Possible Answers:

$\bigtriangleup DEF$ is an equilateral triangle.

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

$\bigtriangleup DEF$ 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 #261 : 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:

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

30 + N

30 - N

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

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 #61 : Geometric Measurement: Recognizing Perimeter

What is the perimeter of the polygon below?

Possible Answers:

48in

46in

47in

45in

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 #11 : Plane Geometry

What is the perimeter of the polygon below?

Possible Answers:

31in

30in

33in

32in

38in

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 #262 : Problem Solving

What is the perimeter of the polygon below?

Possible Answers:

41in

43in

42in

44in

40in

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 #9 : Parallelograms

What is the perimeter of the polygon below?

Possible Answers:

54in

51in

52in

55in

53in

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 #251 : Geometry

What is the perimeter of the polygon below?

Possible Answers:

40in

41in

44in

42in

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 #11 : How To Find The Perimeter Of A Figure

What is the perimeter of the polygon below?

Possible Answers:

34in

35in

36in

37in

38in

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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HSPT Math : How to find the perimeter of a figure

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #261 : Problem Solving

Example Question #263 : Problem Solving

Example Question #62 : Geometry

Example Question #261 : Problem Solving

Example Question #61 : Geometric Measurement: Recognizing Perimeter

Example Question #11 : Plane Geometry

Example Question #262 : Problem Solving

Example Question #9 : Parallelograms

Example Question #251 : Geometry

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

All HSPT Math Resources

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