Find the area of a rhombus whose smaller diagonal is 6 cm and the side is 5 cm.

univerkov | August 5, 2021 | education

Let ABCD be a given rhombus, point O – the point of intersection of the diagonals of the rhombus, AC = 6 cm, AB = 5 cm.

Triangle AOB – rectangular (diagonals of the rhombus intersect at right angles).

AO = 1/2 * AC = 3 cm, since the diagonals are halved by the point of intersection.

According to the Pythagorean theorem: BO² = AB² – AO² = 5² – 3² = 25 – 9 = 16. BO = 4 cm.

ВO is half of BD, BD = 4 * 2 = 8 cm.

The area of a rhombus is calculated by the formula S = 1/2 * d1 * d2 (d1 and d2 are the diagonals of the rhombus).

S (ABCD) = 1/2 * AC * BD = 1/2 * 6 * 8 = 24 cm².

Answer: the area of the rhombus is 24 cm².

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