An equilateral triangle measures 9 inches on each side its area is?

Answer 1

(81/4)*(sqrt(3))

The area of a triangle is expressed by 1/2 bh, where b is the base length of the triangle, and h is the vertical height. In this instance, the base is equal to 9. The height of an equilateral triangle can be found using the Pythagorean theory with a being half the length of one side of the equilateral triangle, h being the height, and c (the hypotenuse) being the length of one side of the equilateral triangle.

Thus,

a2+h2=c2

(9/2)2+h2=(9)2

h2=81-(81/4)
h=9(sqrt(3))/2

So, A=1/2 bh=1/2 (9)(9(sqrt(3))/2)=(81/4)*(sqrt(3))

Area = 1/2 * length * height

height is square root 2(9)2 = square root 2(81)=square root 192 = 13.85640646...

1/2 * 13.85640646 * 9 = 62.3538290 est. to 62.3 square inch