HSPT Math : How to find the perimeter of a figure

Study concepts, example questions & explanations for HSPT Math

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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 \displaystyle a-1?

Possible Answers:

\displaystyle 4a+4

\displaystyle a^2-4

\displaystyle 4a^2-4

\displaystyle 4a-4

\displaystyle a-4

Correct answer:

\displaystyle 4a-4

Explanation:

Write the perimeter formula for a square.

\displaystyle P=4s

Substitute the side length in the formula and simplify.

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

Example Question #263 : Problem Solving

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

Possible Answers:

\displaystyle 25 \pi

\displaystyle 2 0 \pi

\displaystyle 40 \pi

\displaystyle 80 \pi

Correct answer:

\displaystyle 40 \pi

Explanation:

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

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

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

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

Example Question #61 : Geometry

\displaystyle \bigtriangleup ABC \sim \bigtriangleup DEF.

\displaystyle \angle B is a right angle.

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

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

Possible Answers:

\displaystyle \bigtriangleup DEF is an equilateral triangle.

\displaystyle \bigtriangleup DEF is a scalene triangle.

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

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

Correct answer:

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

Explanation:

Corresponding angles of similar triangles are congruent, so 

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

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

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

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

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

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

\displaystyle \overline{EF} \cong \overline{DE}

making \displaystyle \bigtriangleup DEF isosceles.

Example Question #263 : Problem Solving

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

Possible Answers:

\displaystyle 30 + N

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

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

\displaystyle 30 - N

Correct answer:

\displaystyle \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 \displaystyle N feet, and the line from the bottom of the ladder horizontally to the house, whose length we will call \displaystyle M feet. See the diagram below.

Ladder

 

 

 

 

By the Pythagorean Theorem,

\displaystyle M^{2}+N^{2} = 30 ^{2} = 900

Solving for \displaystyle M:

\displaystyle M^{2}+N^{2} - N^{2} = 900 - N^{2}

\displaystyle M^{2}= 900 - N^{2}

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

Example Question #1 : Parallelograms

What is the perimeter of the polygon below? 

A

 

Possible Answers:

\displaystyle 46in

\displaystyle 45in

\displaystyle 43in

\displaystyle 48in

\displaystyle 47in

Correct answer:

\displaystyle 48in

Explanation:

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

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

Example Question #1871 : Common Core Math: Grade 3

What is the perimeter of the polygon below? 

B

 

Possible Answers:

\displaystyle 30in

\displaystyle 32in

\displaystyle 31in

\displaystyle 38in

\displaystyle 33in

Correct answer:

\displaystyle 32in

Explanation:

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

\displaystyle 8+7+4+1+4+8=32

Example Question #1872 : Common Core Math: Grade 3

What is the perimeter of the polygon below? 

C

 

Possible Answers:

\displaystyle 43in

\displaystyle 42in

\displaystyle 44in

\displaystyle 41in

\displaystyle 40in

Correct answer:

\displaystyle 42in

Explanation:

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

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

Example Question #1873 : Common Core Math: Grade 3

What is the perimeter of the polygon below? 

D

 

Possible Answers:

\displaystyle 54in

\displaystyle 55in

\displaystyle 52in

\displaystyle 51in

\displaystyle 53in

Correct answer:

\displaystyle 52in

Explanation:

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

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

Example Question #1874 : Common Core Math: Grade 3

What is the perimeter of the polygon below? 

E

 

Possible Answers:

\displaystyle 42in

\displaystyle 40in

\displaystyle 41in

\displaystyle 43in

\displaystyle 44in

Correct answer:

\displaystyle 40in

Explanation:

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

\displaystyle 8+12+4+6+4+6=40

Example Question #1875 : Common Core Math: Grade 3

What is the perimeter of the polygon below? 

F

 

Possible Answers:

\displaystyle 35in

\displaystyle 37in

\displaystyle 34in

\displaystyle 38in

\displaystyle 36in

Correct answer:

\displaystyle 38in

Explanation:

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

\displaystyle 7+7+2+5+5+12=38

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