SOLUTION: How do i find the area of a regular polygon with an exterior angle 30° and a side length of 10 inches I really need help. I just want to learn how u got the answer. Please help me

Algebra ->  Polygons -> SOLUTION: How do i find the area of a regular polygon with an exterior angle 30° and a side length of 10 inches I really need help. I just want to learn how u got the answer. Please help me      Log On


   

Question 1023784: How do i find the area of a regular polygon with an exterior angle 30° and a side length of 10 inches
I really need help. I just want to learn how u got the answer. Please help me understand how u got the answer
Found 2 solutions by Fombitz, richard1234:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
S=G%2F2
S%2BG=90
Substituting,
G%2F2%2BG=90
%283%2F2%29G=90
G=90%282%2F3%29
Now solve for G, then use either equation to solve for S.

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
There are 12 sides to the polygon, since the sum of the exterior angles of a convex polygon is 360°.

You can draw the center and split into 12 congruent triangles, so you only need to find the area of one of them. Draw an altitude from the center to one of the sides (apothem), and note that the base is 10 and the height h satisfies tan 75 = h/5 or h = 5 tan 75. Use that to find the area of one triangle, then multiply by 12.