Question

The polygons are regular polygons. Find the area of the shaded region.

Answer 1

Polygon area = [circumradius^2 * # sides * sine (360/# sides)] / 2
small hexagon area =[5^2 * 6 * sine (60)] / 2
small hexagon area =[25 * 6 * 0.86603] / 2
small hexagon area = 64.95225 sq feet

large hexagon area =[10^2 * 6 * sine (60)] / 2
large hexagon area =[600 * 0.86603] / 2large hexagon area = 259.809 sq feet
Area of shaded region = large hexagon area -small hexagon areaArea of shaded region = 259.809 -64.95225 Area of shaded region = 194.85675 sq feet

Source:http://www.1728.org/polygon.htm