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Kryger [21]
3 years ago
11

Find the area of the

Mathematics
1 answer:
e-lub [12.9K]3 years ago
5 0

Answer:

E) 613.9 m2

Step-by-step 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

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