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

The apothem of an equilateral triangle is the short leg of a special triangle .

From the figure as shown below:

s be the side of an equilateral triangle

a be the apothem of an equilateral tiangle

then;

or

As per the given statement:

apothem(a) = 6 inch.

= inch.

To find the area of an equilateral triangle:

Area of an equilateral triangle is given by;

where

A is the area of an equilateral triangle and s be the sides of an equilateral triangle.

Substitute the given values we have;

square inches.

Therefore, the area of an equilateral triangle is, square inches.

for the points

step-by-step explanation:

answer: the angel abc is 30°,and the abc is a triangle where the angel bac is 90°

so ac is the half of 24=12ft,and from the pythagorean theorem we find ba

ba=√bc^2-ac^2=√576-144=√432=12√3ft

so bac is 12+12√3=12(1+√3)ft