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Problem 557

# Find the area of a regular hexagon if one side has the length of 6

### Short Answer

Expert verified
The area of the regular hexagon is $$54\sqrt{3}$$.
See the step by step solution

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## Step 1: Find the area of one equilateral triangle

To find the area of one equilateral triangle, we can use the formula: Area = (side length^2 * sqrt(3)) / 4 In this exercise, the side length is 6. Area = (6^2 * sqrt(3)) / 4 Area = (36 * sqrt(3)) / 4 Area = 9 * sqrt(3)

## Step 2: Find the area of the hexagon

Now that we've found the area of one equilateral triangle, we can find the area of the hexagon by multiplying the area of one triangle by 6: Hexagon Area = 6 * (9 * sqrt(3)) Hexagon Area = 54 * sqrt(3) The area of the regular hexagon is 54 * sqrt(3).

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