SOLUTION: the number of diagonals of a regular polygon is 35. find the area if it's apothem is 15

Question 1164596: the number of diagonals of a regular polygon is 35. find the area if it's apothem is 15
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
The number of diagonals of an n-sided polygon is: (n/2)(n-3)
Thus, n/2(n-3) = 35 -> (n-10)(n+7) = 0 -> n = 10 (take the positive solution)
The polygon is made up of 10 triangles, with altitude equal to the apothem
The interior angles of a decagon are 144 deg.
The base of each triangle, b = 2a/tan(144/2), where a = the apothem
So the area of each triangle = a/tan(72)*a = 15^2/tan(72)
Thus the entire area is 10*15^2/tan(72) = 731.07
RELATED QUESTIONS
The number of diagonals of a regular polygon is 35. Find the area of the polygon if its... (answered by AnlytcPhil)

the number of diagonals of a regular polygon is 56 in.find the perimeter of the polygon... (answered by ikleyn)

How do you find the area of a regular polygon if you only have the... (answered by shree840)

The perimeter of a regular polygon is 48 and its apothem is 6.What is the area of the... (answered by savvyhush23)

if polygon A and polygon B are similar regular polygons,what will be the measure of the... (answered by ikleyn,ise)

find the side length of a 15-sided regular polygon with apothem a=6 and area A= 282... (answered by Alan3354)

Each interior angle of a regular polygon is 160�. Find the number of... (answered by J2R2R)

How do I find the Apothem of a regular polygon? The equation i am trying to use is to... (answered by solver91311)

I want to find the area of a regular pentagon and I only have the apothem. Can I do... (answered by htmentor)