Question

find the area of a regular pentagram if one of the sides of inner pentagon is 3cm

Answer 1

To find the area of a pentagon we use the formula (where s = side):
https://en.wikipedia.org/wiki/Pentagon
AREA = s^2 * square root (25 + 10 * sqrt(5)) /4
AREA = 9 * sq root (25 + 22.361) / 4
AREA = 9 * 6.8819 / 4
AREA = 61.9371 / 4
PENTAGON AREA = 15.484

The pentagon is surrounded by 5 isosceles triangles whose height is calculated by
tan (72 degrees) = height / 1.5
height = 3.0777 * 1.5
height = 4.6166

and the area of EACH triangle equals
1.5 * 4.6166 = 6.9249

AREA of all 5 triangles = 34.625 PLUS
PENTAGON AREA = 15.484

TOTAL PENTAGRAM AREA = 50.109

Answer 2

thanks ^_^