Find the area of a rhombus with a side of 5 cm and a diagonal of 6 cm.

1. The tops of the rhombus – A, B, C, D. Diagonal BD = 6 cm. The side of the rhombus is 5 cm.

2. Calculate the area of the triangle ABD (S) using Heron’s theorem:

S = √P (P – AB) (P – BD) (P – AD). P – half of the perimeter. P = (5 + 5 + 6) / 2 = 8 cm.

S = √8 x 3 x 2 x 3 = √144 = 12 cm².

3. A rhombus with a diagonal BD is divided into two equal triangles: ABD and BCD, therefore its area is 2 times the area of triangle ABD, that is, equal to 12 x 2 = 24 cm².

Answer: the area of the rhombus is 24 cm².