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