A pentagon’s radius (measure from center to vertex) measures 4 cm, what is the pentagon’s area?

Question

I have to use this method to answer this question which is : 360 / 6 = 60

60 = top of one angle

180 - 60 = 120, 120 / 2 = 60

60 = side angle

Area = 1/2*Base*Height

tan (60) = h (10/2)

h = 5 * tan (60), h = 8.66

A = 1/2 (10) (8.66)

A = 43.3

43.3 * 6 = 259.8

Answer 1

The total number of degrees is (5-2)*180 = 3 * 180 = 540

So there are 540/5 = 108 degrees at each vertex

each pie slice has base angles 54 degrees each

dropping the height from center perpendicular to edge

sin 54 = h/4

h = 4 * sin 54 = 3.2360679775-

while cos 54 = x/4 ---> x = 4 * cos 54 = 2.351141+

multiplying these decimal numbers and cutting in half, the

area of the slice is

3.80422605034366375

Multiplying by 5 gives a total area of just over 19