Find the area of the regular figure below:

A) 645.4 m2
B) 571.3 m2
C) 624.7 m2
D) 590.2 m2
E) 613.9 m2

explain pls

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

E) 613.9 m2

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation:

i do not know the answer

step-by-step explanation: