Question

Find the area of a triangle whose vertices are 

 (a, c + a), (a, c) and (−a, c − a)

Answer 1

We know area of triangle formed by three points (x₁y₁) , (x₂y₂), and (x₃y₃)is given by `triangle=1/2 [x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]`

The vertices are given as  (a, c + a), (a, c) and (−a, c − a)  

Δ = 1/2[a (c-c+a) + a(c-a-c-a)-a(c+a-c) 

   = 1/2[a(a)+a(2a)-a(a)] 

   = 1/2 [-2a²]=a²