Question

Find the area of the regular polygon.
Round to the nearest tenth.
5 square root of 3cm

Answer 1

5 square root 3= 8.66
8.66 x 6 = 51.96

Answer 2

Based on the given shape, the area of the regular hexagon is approximately 194.9
`cm^2`.

How to find the area of a regular polygon

To find the area of a regular hexagon given the length from one flat edge (apothem) to the center, you can use the formula:

Area of hexagon = (3 * √3 / 2) *
`apothem^2`

Given that the length from one flat edge to the center (apothem) is 5√3 cm:

Area of hexagon = (3 * √3 / 2) *
`(5\sqrt3)^2`

Area of hexagon = (3 * √3 / 2) * 75

Area of hexagon = 225√3 / 2

Area of hexagon = 112.5√3

Approximating this numerical value:

112.5 * 1.732 ≈ 194.86

Rounded to the nearest tenth, the area of the regular hexagon is approximately 194.9
`cm^2`.