SOLUTION: URGENT HELP NEEDED! PLEASE SHOW WITH WORKINGS! A regular hexagon is circumscribed about a circle with a radius of 3 cm with centre O. (a) What is angle EOD? (b) Find the area o

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Question 870828: URGENT HELP NEEDED! PLEASE SHOW WITH WORKINGS!
A regular hexagon is circumscribed about a circle with a radius of 3 cm with centre O.
(a) What is angle EOD?
(b) Find the area of triangle EOD and hence find the area of the hexagon ABCDEF.
Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website!
note that a hexagon has 6 sides and made up of 6 equalaterial triangles
a) angle EOD = 360 / 6 = 60 degrees
b) divide one of the equilateral triangles in half and we get a 30, 60, 90 right triangle. we know the altitute of the new triangle is 3 cm and we can calculate its base by tan(60) = altitude / base = 3 / base and
base = 3 / tan(60) = 1.73 cm, therefore the area of the new triangle is
area = (1/2)*(1.73)*3 = 2.60 cm^2
now the area of EOD is 2 * 2.60 = 5.2 cm^2, and
area of ABCDEF is 6*(5.2) = 31.2 cm^2