Question

formula of area of isosceles triangle in heron's formula

Answer 1

Let a,b and c are the sides of the triangle.

As the triangle is isosceles, let a = b.

2s = a + b + c = 2a + c

Area of the triangle = √s(s–a)(s–b)(s–c)

=√(a+c/2)(a+c/2–a)(a+c/2–b)(a+c/2–c)

=√(a+c/2)(c/2)(a+c/2–a)(a+c/2–c)

=√(a+c/2)(c2/4)(a–c/2)

=(c/2)√(a2–c2/4)