SOLUTION: The area of a convex regular polygon is 192√3 cm2. The polygon has nine diagonals. Find the perimeter of the polygon, in centimeters

Algebra ->  Polygons -> SOLUTION: The area of a convex regular polygon is 192√3 cm2. The polygon has nine diagonals. Find the perimeter of the polygon, in centimeters      Log On


   

Question 1066704: The area of a convex regular polygon is 192√3 cm2. The polygon has nine diagonals. Find the perimeter of the polygon, in centimeters
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The number of sides of a polygon using the number of diagonals is,
D=S%28S-3%29%2F2
9=S%28S-3%29%2F2
S%5E2-3S=18
S%5E2-3S-18=0
%28S-6%29%28S%2B3%29=0
S-6=0
S=6
So it's a hexagon.
A%5BHEX%5D=+%283%2F2%29sqrt%283%29X%5E2
%283%2F2%29sqrt%283%29X%5E2=196sqrt%283%29
X%5E2=392%2F3
X=sqrt%28392%2F3%29
X=%2814%2F3%29sqrt%286%29
So the perimeter is then,
P=6X
P=28sqrt%286%29cm