Question

Find the area of an equilateral triangle (regular 3-gon) with the given measurement.

6-inch apothem

A = sq. in.

Answer 1

area=A^2*N*tan(pi/N)
A= length of apothem=6
N=no. of sides=3
pi/N=180/3=60

area=6^2*3*tan(60)
=36*3*sqrt(3)
=108sqrt(3)

Answer 2

ap=6, area A=bh/2, base b=2ap*sqrt3, height h=3ap
A=bh/2
A=(2apsqrt3)(3ap)/2
A=3(ap)^2 sqrt3
A=3*36*sqrt3=187.06 square inch