The parallelogram diagonals of 6 cm and 14 cm intersect at an angle of 60 °. Find the area of the parallelogram.

The diagonals of the parallelogram at the intersection point are halved and divide it into four equal triangles.

Then DO = BO = BD / 2 = 6/2 = 3 cm, CO = AO = AC / 2 = 14/2 = 7 cm.

Sod = OС * OD * Sin60 / 2 = 7 * 3 * √3 / 4 = 21 * √3 / 4.

Then Savsd = 4 * Ssod = 4 * 21 * √3 / 4 = 21 * √3 cm2.



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