Question

A regular hexagon has sides of 3 feet. What is the area of the hexagon

Answer 1

To find the area of a regular hexagon with sides of 3 feet, we can use the formula: Area = (3/2) x (apothem) x (side length). By drawing radii to adjacent vertices and creating an equilateral triangle, we can find the apothem to be (3√3)/2. Substituting these values into the formula, we find that the area of the hexagon is 9√3 square feet.

Step-by-step explanation:

To find the area of a regular hexagon, we can use the formula:

Area = (3/2) x (apothem) x (side length)

Since the hexagon has sides of 3 feet, the side length is 3. To find the apothem, which is the distance from the center of the hexagon to any of its sides, we can draw two radii to two adjacent vertices, creating an equilateral triangle with side length 3. The apothem of this triangle is equal to (√3/2) x 3 = (3√3)/2. Substituting these values into the formula, we get:

Area = (3/2) x (3√3)/2 x 3

Simplifying, we find that the area of the hexagon is 9√3 square feet.

Answer 2

We are asked to solve for the area of the regular hexagon and we already know that regular hexagon has a 6 equal side. To answer this problem, we need to apply the formula below:
Area of hexagon = (3√3 / 2)*a² where a is the measurement of the side
Since the side measurement is given, we can directly substitute it to the formula such as:
Area = (3√3 /2)* (3feet)²
Area = 23.38 feet²

The answer is 23.38 feet².