Question

Find the area of a regular 12-sided polygon with side of length s and apothem 8.

(Give your answer in terms of s.)

Answer 1

`If\ this\ is\ regular\ 12-sides\ polygon\ it\ is\ build\ from\ 12\ isosceles\\triangles.\\\\ apothem=height\ of\ triangle\\\ side=base\ of\ triangle\\\\ Area\ of\ one\ triangle:\\ A=(s*apothem)/(2)=(s*8)/(2)=4s\\\\ Area\ of\ polygon\ =12*A=12*4s=48s`

Answer 2

apothem is the height of a triangel formed by two consecutive vertices with the center. the are of this triangle = 1/2 s 8 = 4s
there area 12 such triangles in the regular 12 side polygon
So area = 12 * 4 s = 48 s