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HSPT Math : How to find the perimeter of a figure

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Example Questions

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

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

Possible Answers:

a-4

a^2-4

4a+4

4a-4

4a^2-4

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:

$25 \pi$

$2 0 \pi$

$40 \pi$

$80 \pi$

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 #61 : 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.

$\bigtriangleup DEF$ is a scalene triangle.

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

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

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 #12 : How To Find The Perimeter Of A Figure

What is the perimeter of the polygon below?

Possible Answers:

45in

46in

48in

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 #1 : Parallelograms

What is the perimeter of the polygon below?

Possible Answers:

32in

31in

30in

33in

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 #13 : How To Find The Perimeter Of A Figure

What is the perimeter of the polygon below?

Possible Answers:

42in

43in

41in

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 #2 : Parallelograms

What is the perimeter of the polygon below?

Possible Answers:

55in

54in

53in

51in

52in

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 #63 : Geometry

What is the perimeter of the polygon below?

Possible Answers:

44in

40in

43in

41in

42in

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 #12 : How To Find The Perimeter Of A Figure

What is the perimeter of the polygon below?

Possible Answers:

35in

38in

34in

36in

37in

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 #11 : How To Find The Perimeter Of A Figure

Example Question #263 : Problem Solving

Example Question #61 : Geometry

Example Question #263 : Problem Solving

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

Example Question #1 : Parallelograms

Example Question #13 : How To Find The Perimeter Of A Figure

Example Question #2 : Parallelograms

Example Question #63 : Geometry

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

All HSPT Math Resources

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