Question

A regular hexagon has sides of 5 feet. What is the area of the hexagon

Answer 1

The area of a regular hexagon with side length of 5 feet is approximately 64.95 square feet. This is computed using the formula for the area of a regular polygon.

Step-by-step explanation:

To calculate the area of a regular hexagon with side length of 5 feet, we can use the formula for the area of a regular polygon, which is A = ¾ n × s2 × cot(π/n), where n is the number of sides and s is the side length. Since a hexagon has 6 sides, we'll have:

A = ¾ × 6 × 52 × cot(π/6)

First, calculate 52 which is 25. The cotangent of π/6 (cot(30 degrees)) is √3. Substituting the values into the formula, we get:

A = ¾ × 6 × 25 × √3 ≈ 64.95 square feet

Therefore, the area of the hexagon is approximately 64.95 square feet.

Answer 2

`a=5ft\\\\Area\ of\ the\ haxagon:A=6\cdot(a^2\sqrt3)/(4)=(3a^2\sqrt3)/(2)\\\\A=(3\cdot5^2\sqrt3)/(2)=(3\cdot25\sqrt3)/(2)=(75\sqrt3)/(2)\ (ft^2)`