SAT Math : How to find the length of a side of a polygon

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #104 : Plane Geometry

If the following shape was going to be drawn in a circle, what is the minimum radius of the circle?

Possible Answers:

8

7

11

9

10

Sat_math_picture3


Correct answer:

7

Explanation:

IF you draw the longest diagonal across the shape, the length of it is 13.4. This means the radius must be at least 6.7. The answer is 7.

Example Question #1 : Other Polygons

Octagon 3

Each side of the above octagonal track is 264 feet in length. Julie starts at point A and runs clockwise at a steady speed of nine miles an hour for nine minutes. When she is finished, which of the following points is closest to her?

Possible Answers:

Point F

Point D

Point E

Point C

Point G

Correct answer:

Point D

Explanation:

Julie runs for nine minutes, or  hour; she runs nine miles per hour. Setting  and  in the rate formula, we can evaluate distance in miles:

Julie runs  miles, which converts to feet by multiplication by 5,280 feet per mile:

 feet.

Each side of the octagonal track measures 264 feet, so Julie runs

sides of the track; this is equivalent to running the entire track three times, then three more sides. She is running clockwise, so three more sides from Point A puts her at Point D. This is the correct response.

 

 

 

Example Question #1 : How To Find The Length Of A Side Of A Polygon

Octagon

Plato High School has an unusual track in that it is shaped like a regular octagon. The track has a perimeter of two-fifths of a mile.

Boris starts at Point A and runs clockwise until he gets halfway between Point E and Point F. Which of the following responses comes closest to the number of feet he runs? 

Possible Answers:

1,200 feet

1,400 feet

1,300 feet

1,500 feet

1,100 feet

Correct answer:

1,200 feet

Explanation:

 One mile comprises 5,280 feet; the perimeter of the track, two-fifths of a mile, is equal to

 feet.

Each (congruent) side of the octagonal track measures one-eighth of this,

 feet.

By running clockwise from Point A to halfway between Point E and Point F, Boris runs along four and one half sides, each of which has this length, for a total running distance of

 feet. 

Of the five responses, 1,200 comes closest.

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