# Find the area of an equilateral triangle (regular 3-gon) with the given measurement. 6-inch apothem A = sq. in.

Find the area of an equilateral triangle (regular 3-gon) with the given measurement. 6-inch apothem A = sq. in.

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6-inch apothem, xxxxxxx x x x

an xxxxxxxxxxx triangle has 6 (30-60-90) triangles each with the xxxxxxxx side xxxxx xxx apothem xx length x x inch

xxxxxxxxx xxxxxxxx xx a is xx xxxxxxxx

sin xx = xxxxxxxxxxxxxxxxxxx x a/hyp = 6/hyp

0.5 = 6/hyp

xxxxxx = x

hyp x 12 xxxxxx

xxxx we need xxxxxx xx xxxx side ,

cos xx x base/hypotenuse = xxxxxxx

xxxxxxxxx x xxxxxxx

xxxxxxxxxxx x xxxx

xxxxxxxx = xxxx

Now, xxxx xx xxxxxx small xxxxxxxx is

xxxxxxxxxxxxxxxxxxxx = 18sqrt(3) sq in

xxxx xxxxxxxxxxx triangle has x such xxxxx xxxxxxxxxx

xxxxxx

area xx equilateral xxxxxxxx = 6*(18sqrt(3)) x xxxxxxxxxx xx in.

= xxxxx sq. xxx xxxxxxx xx xxxxxxx xxxxxx