How to find the length of a side of a polygon
SAT Math · Learn by Concept
Help Questions
SAT Math › How to find the length of a side of a polygon
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?
1,200 feet
1,100 feet
1,300 feet
1,400 feet
1,500 feet
Explanation
One mile comprises 5,280 feet; the perimeter of the track, two-fifths of a mile, is equal to
Each (congruent) side of the octagonal track measures one-eighth of this,
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
Of the five responses, 1,200 comes closest.
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?
Point D
Point E
Point F
Point G
Point C
Explanation
Julie runs for nine minutes, or 
Julie runs 
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.
If the following shape was going to be drawn in a circle, what is the minimum radius of the circle?
7
8
9
10
11
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.