To find the area of a regular pentagon (a five-sided polygon) with a given side length, we can use the formula:
Area = (1/4) * √(5(5 + 2√5)) * s²
where s is the length of a side of the pentagon. In this case, the side length is 6 m.
Substituting the value of s into the formula, we get:
Area = (1/4) * √(5(5 + 2√5)) * (6)²
First, calculate (6)²:
(6)² = 36
Now, let’s solve the part under the square root:
5 + 2√5 ≈ 5 + 4.472 = 9.472
Now, multiply this by 5:
5(9.472) = 47.36
Next, we take the square root of 47.36:
√(47.36) ≈ 6.88
Now substitute back:
Area = (1/4) * 6.88 * 36
Calculating that gives:
Area ≈ (1/4) * 247.68 ≈ 61.92
Therefore, the area of the regular pentagon with a side length of 6 m is approximately 61.92 m².