Are of an equilateral triangle

Question

Find the area of an equ. triangle with a apothem of 2ft.

Answer 1

For an equilateral triangle, the apothem is 1/3 of the height, so the height is 3 times 2 ft or 6 ft.

The base of the equilateral triangle is the apothem times 2√3 or 2ft times 2√3 = 4√3ft.

So the area of the triangle is (1/2)(base)(height) or

(1/2)(4√3ft)(6 ft) = 12√3ft².

 

 

Answer 2

For a regular polygon

 

A = 0.5(a)(p), where a = apothem, p = perimeter

 

A = 0.5(2)p

A = p

Answer 3

An equilateral triangle has sides of equal length.

 

The apothem of the triangle is equivalent to half the triangle's height.  the area of a triangle is bh/2.

 

Area = (2*2)b / 2

Area = 2b

 

where b is the side of the triangle.