Have a look here: Pentagram - Wikipedia, the free encyclopedia
Have a look here: Pentagram - Wikipedia, the free encyclopedia
Hello, leart369!
I have a very "clunky" solution . . .
i need to find the area of the star only knowing the radius of the circle: R=1
Label the vertices starting at the top and moving clockwise.
. . Draw segments
Let be the center.
Consider the area of one-fifth of the star, quadrilateral
The area of a triangle is given by: .
. . (one-half the product of two sides and the sine of the included angle)
The area of
The area of
. . The area of quad
Therefore: .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
We know that . Can we find . . . . Yes!
Substitute [1] into [2]: .
. .