SOLUTION: if a regular hexagon has a perimeter of 150 m. What is its area?

Question 404286: if a regular hexagon has a perimeter of 150 m. What is its area?
Found 2 solutions by Alan3354, richard1234:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Each side is 25 meters (150/6)
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n = # of sides, s = side length

Area =~ 64.952 sq meters

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Since the perimeter of the hexagon is 150 m, it follows that each side length is 25 m and the area of the hexagon is equal to six times the area of an equilateral triangle of length 25.

We could find the area of such an equilateral triangle by drawing an altitude to the base, etc. but it's a little ugly and uninteresting. A quick way to do it is to use where is between sides a and b. Thus,

Multiplying by 6, we obtain .
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