To find the area of a regular hexagon, we can use the formula:
Area = (3√3 / 2) × r²
where r is the radius of the hexagon. In this case, the radius is 4.
Substituting the value of the radius into the formula, we get:
Area = (3√3 / 2) × (4)²
Calculating the square of the radius:
4² = 16
Now we substitute this back into the area formula:
Area = (3√3 / 2) × 16
This simplifies to:
Area = 24√3
To get an approximate numeric value, we can use the approximate value of √3, which is about 1.732:
Area ≈ 24 × 1.732 ≈ 41.568
Therefore, the approximate area of the hexagon is about 41.57 square units.