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SAT Math : Pentagons

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Example Question #11 : Geometry

Pentagon

The above diagram shows a pentagonal track with perimeter one third of a mile. Adrianne starts at Point A and runs clockwise until she gets halfway between Points D and E. Which of the following choices is closest to the number of feet she runs?

Possible Answers:

1,200 feet

1,400 feet

1,000 feet

1,300 feet

1,100 feet

Correct answer:

1,200 feet

Explanation:

The perimeter of the pentagonal track is one third of a mile; one mile is equal to 5,280 feet, so the perimeter is

$\frac{1}{3} \times 5, 280 = 1,760$ $\displaystyle \frac{1}{3} \times 5, 280 = 1,760$ feet.

Each side of the pentagon has length one fifth of its perimeter, or

$\frac{1}{5} \times 1,760 = 352$ $\displaystyle \frac{1}{5} \times 1,760 = 352$ feet.

Adrianne runs three and one half sides, or

$3 \frac{1}{2} \times 352 = 1,232$ $\displaystyle 3 \frac{1}{2} \times 352 = 1,232$ feet.

This makes 1,200 feet the closest, and correct, choice.

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Example Question #1 : Pentagons

Pentagon

Aristotle High School has an unusual track in that it is shaped like a regular pentagon. Each side of the pentagon measures 264 feet.

Benny runs at a steady speed of eight miles an hour for ten minutes, starting at point A and working his way clockwise. When he is finished, which of the following points is he closest to?

Possible Answers:

Point E

Point A

Point D

Point B

Point C

Correct answer:

Point C

Explanation:

Benny runs at a rate of eight miles an hour for ten minutes, or $\frac{10}{60} = \frac{1}{6}$ $\displaystyle \frac{10}{60} = \frac{1}{6}$ hours. The distance he runs is equal to his rate multiplied by his time, so, setting $r = 8 , t = \frac{1}{6}$ $\displaystyle r = 8 , t = \frac{1}{6}$ in this formula:

d = rt $\displaystyle d = rt$

$d = 8 \cdot \frac{1}{6} = \frac{4}{3}$ $\displaystyle d = 8 \cdot \frac{1}{6} = \frac{4}{3}$ miles.

One mile comprises 5,280 feet, so this is equal to

$\frac{4}{3} \cdot 5,280 = 7,040$ $\displaystyle \frac{4}{3} \cdot 5,280 = 7,040$ feet.

Since each side of the track measures 264 feet, this means that Benny runs

$7,040 \div 264 = 26 \frac{2}{3}$ $\displaystyle 7,040 \div 264 = 26 \frac{2}{3}$ sidelengths.

This means Benny runs around the track for 25 sidelengths, which is 5 complete times, back to Point A; he then runs one more complete sidelength to Point B; and, finally, he runs $\frac{2}{3}$ $\displaystyle \frac{2}{3}$ of a sidelength, finishing closest to Point C.

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Example Question #11 : Sat Mathematics

Find the sum of all the angles in a pentagon.

Possible Answers:

540 $\displaystyle 540$

720 $\displaystyle 720$

900 $\displaystyle 900$

360 $\displaystyle 360$

Correct answer:

540 $\displaystyle 540$

Explanation:

To solve, simply use the formula to find the total degrees in a polygon, where n is thenumber of vertices.

In this particular case, a pentagon is a shape that has five sides and thus has five vertices.

Thus,

$\displaystyle degrees=(n-2)*180=(5-2)*180=3*180=540$

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SAT Math : Pentagons

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #11 : Geometry

Example Question #1 : Pentagons

Example Question #11 : Sat Mathematics

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