Question

solve the question given below

Answer 1

The height of an equilateral triangle of side a is given by h = sqrt(a^2 - (a/2)^2) = sqrt(3a^2/4) = a(sqrt(3))/2.

Length of side of equilateral triangle a is obtained by equating a(sqrt(3))/2 = 9 =>

a = (2x9)/sqrt(3) = 18(sqrt(3))/(sqrt(3))^2 = 18(sqrt(3))/3 = 6(sqrt(3)).

Area of equilateral triangle = (1/2)(a(sqrt(3))/2)(a/2) = a^2(sqrt(3))/4 = (sqrt(3))/4[6(sqrt(3))]^2 = (36x3)(sqrt(3))/4 = 27(sqrt(3)) = 46.765 sq cm.