Find the area of a rhombus if its vertices are A (3, 0), B (4, 5), C (– 1, 4) and D (– 2, – 1).

As the diagonal of rhombus divides it into two parts, it is sufficient to calculate the area of one part and double it.


Consider, the Diagonal AC,


Then,


ar(ABCD) = 2× ar(ΔABC)


Now,


A = (3,0); B = (4, 5); C = (– 1, 4)


As we know area of triangle formed by three points (x1, y1), (x2, y2) and (x3, y3)




=6 square units


ar(ABCD) = 2× ar(ΔABC) = 2(6) = 12 square units


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