8 The distance from the center of a regular hexagon to verte

8. The distance from the center of a regular hexagon to vertex if 15 cm. Find the area of the regular hexagon. Round to the nearest tenth

Solution

The side of a hexagon is equal to the distnace from vertex to center of hexagon, this is because hexagon with its consecutive points forms a equilateral triangle with the vertex.

If side of a hexagon is a , then its area is 3sqrt(3)*a^2 / 2

So, area of hexagon is 3*sqrt(3)*15^2/2

= 584.6 cm^2