Answer :


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


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