All SAT Math Resources
Example Questions
Example Question #13 :Geometry
Archimedes High School has an unusual track in that it is shaped like a regular hexagon, as above. Each side of the hexagon measures 264 feet.
Alvin runs at a steady speed of seven miles an hour for twelve minutes, starting at point A and working his way clockwise. When he is finished, which of the following points is he closest to?
Point C
Point B
Point D
Point F
Point E
Point E
Alvin runs at a rate of seven miles an hour for twelve minutes, orhours. The distance he runs is equal to his rate multiplied by his time, so, settingin this formula:
miles.
One mile comprises 5,280 feet, so this is equal to
feet
Since each side of the track measures 264 feet, this means that Alvin runs
sidelengths.
,
which means that Alvin runs around the track four complete times, plus four more sides of the track. Alvin stops when he is at Point E.
Example Question #14 :Geometry
A circle with circumferenceis inscribed in a regular hexagon. Give the perimeter of the hexagon.
None of these
Below is the figure referenced; note that the hexagon is divided by its diameters, and that an apothem—a perpendicular bisector from the center to one side—has been drawn.
The circle has circumference; its radius, which coincides with the apothem of the hexagon,is the circumference divided by:
The hexagon is divided into six equilateral triangles. One,, is divided by an apothem of the hexagon- a radius of the circle - into two 30-60-90 triangles, one of which is. Sincehas length 30, and it is a long leg of, then short leghas length
is the midpoint of, one of the six congruent sides of the hexagon, so
;
this makes the perimeter of the hexagon six times this, or
.