Find the area of

The triangle has vertices A(2,1), B(4,3), C(2,5).

Now, mid-point of AB = D = = (3,2)

Mid-point of BC = F = = (3,4)

Mid-point of CA = E = = (2,3)

So, the triangle formed by joining the mid-points of the sides of the triangle ABC has vertices (3, 2), (3, 4) and (2, 3).

Area of triangle ABC =

1/2 |[x₁(y₂ – y₃) + x₂(y₃ – y₁) + x₃(y₁ – y₂)]|

= 1/2 |[3(3 - 4) + 3(3 - 2) + 2(2 - 4)

= 1/2 |[-3 + 3 -4]|

= 2/2

= 1 sq. units