SOLUTION: This is a right triangle trigonometry problem. 1. A playground is built in the shape of a regular hexagon. If one side measures 40 meters, what is the area covered by the playg

Algebra ->  Trigonometry-basics -> SOLUTION: This is a right triangle trigonometry problem. 1. A playground is built in the shape of a regular hexagon. If one side measures 40 meters, what is the area covered by the playg      Log On


   

Question 704519: This is a right triangle trigonometry problem.
1. A playground is built in the shape of a regular hexagon. If one
side measures 40 meters, what is the area covered by the playground?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The hexagon can be broken up into 6 equal equilateral triangles

Each equilateral triangle can be broken further into two right triangles with legs 20 (40/2 = 20) and 20*sqrt(3). The area of each right triangle is


A = b*h/2

A = 20*20*sqrt(3)/2

A = 200*sqrt(3)

Now multiply this by 2 (since there are 2 right triangles) to get 400*sqrt(3). Then multiply this by 6 since there are 6 congruent equilateral triangles.

6*400*sqrt(3) = 2400*sqrt(3)

So the answer is 2400*sqrt(3) square meters.

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