Answer:
E) 613.9 m2
Explanation:
sum of measures of interior angles of a polygon of n sides:
(n - 2)180
For a pentagon:
(5 - 2)180 = 3(180) = 540
measure of one interior angle of a regular pentagon:
540/5 = 108
Draw a segment from the center of the pentagon to the top vertex. Now you have a right triangle.
The triangle has a 90 deg angle where the segment in the figure meets the side of the pentagon. Let half of the side of the pentagon be x. x is a side of the right triangle.
For the 54 deg angle in the triangle, 13 m is the opposite leg, and x is the adjacent leg.
tan A = opp/adj
tan 54 = 13/x
x = 13 m/tan 54 = 9.445 m
x is half of the side of the pentagon.
2x is the side of the pentagon.
2x = 2(9.445 m) = 18.89 m
The given 13 m segment is the apothem of the pentagon.
A = nsa/2
where n = number of sides, s = length of 1 side, a = length of apothem
A = (5)(18.89 m)(13 m)/2
A = 613.9 m^2
Answer: E) 613.9 m2