Find the area of a regular pentagon of side length 6m
To find the area of a regular pentagon, we can use the formula:
Area = (1/4) * n * s^2 * cot(π/n)
Where n is the number of sides (in this case, 5) and s is the side length (in this case, 6m).
Plugging in the values, we get:
Area = (1/4) * 5 * 6^2 * cot(π/5)
Calculating further:
Area = (1/4) * 5 * 36 * cot(π/5)
Area = 45 * 36 * cot(π/5)
Now, we'll calculate the cotangent of π/5:
cot(π/5) = 1 / tan(π/5)
Using a calculator, we find that tan(π/5) ≈ 0.7265425
cot(π/5) ≈ 1 / 0.7265425 ≈ 1.376381920
Substituting this value back into the formula:
Area ≈ 45 * 36 * 1.376381920
Area ≈ 2216.4694344 square meters
Therefore, the area of a regular pentagon with side length 6m is approximately 2216.4694344 square meters.