Find the area of a regular pentagon with side equal to 3 and apothem equal to K. 1.5K 7.5K 12K

Question

help me please

Answer 1

The area of a pentagon formula is   A = (5/2)sa   where s is the length of a side and a is the length of an apothem

 

Plugging straight into the formula we have   A = (5/2)(3)(k) = 15/2 k = 7.5k

 

FYI:  Apothem is a line segment from the center of the pentagon to the midpoint of a side.

Answer 2

Draw line segments from the vertices of a side of the pentagon to the center of the polygon. This makes a triangle in which the apothem is the altitude. Since the base of the triangle is 3 and the altitude is K, the area of the triangle is (1/2) * 3 * K = 1.5K. The regular pentagon can be divided into 5 consecutive congruent triangles. So the area of the pentagon is 5 * 1.5K, or 7.5K.