A circular field that measures 100π meters in circumference has six monuments evenly spaced around that circumference. If a hexagonal path has been installed to allow patrons to walk straight from monument to as pictured, what is the length, in meters, of that path.
A. 240
B. 270
C. 300
D. 330
E. 360
The key to solving this question is recognizing that, with six equally spaced items around a circle, the lines connecting the center of the circle to each item will form 60-degree angles (each pair of adjacent lines will form a 1/6 section of the circle). That means that, since you know the circumference of the circle is 100π the radius is 50. And what you're really looking to calculate - the distance from each monument to the next - will then form a set of equilateral triangles with all sides 50. Each monument-to-monument distance will form the third side of an isosceles triangle (each radius is the same) with one angle 60, so they must all be equilateral.
Therefore, the straight-line distance from each monument to the next will be 50, and with six such distances forming the path, the path will total 300 meters in length.