Question

Find the area of the regular polygon. Give the answer to the nearest tenth.

dodecagon with a perimeter of 108 cm

Answer 1

Area of a polygon
= (perimeter/2)*distance from centre to one of the sides.

A dodecagon has 12 sides.
Each side = perimeter/12 = 9
The exterior angle is 360/12=30 degrees
interior angle is 180-30=150 deg.
Base angle of isosceles triangle formed with the base and the centre
= 150/2=75 degrees
Height of triangle = (9/2) tan(75 deg.)
Area of dodecagon
=(108/2)*4.5tan(75deg.)
= 907 approx.