A side and a diagonal of a rhombus are 10cm and 12cm respectively, Find its area

Analyze the question: A rhombus has a side of 10 cm and one diagonal of 12 cm. We need its area.

Concept: The diagonals of a rhombus bisect each other at right angles. This splits the rhombus into 4 congruent right-angled triangles. The area is:

Area = ½ × d₁ × d₂

Solution:

1. Half of the given diagonal = 12 ÷ 2 = 6 cm.
2. Each right-angled triangle has hypotenuse 10 cm (the side of the rhombus) and one leg 6 cm.
3. Find the other leg using Pythagoras: x² = 10² − 6² = 100 − 36 = 64 x = 8 cm
4. So the other diagonal = 2 × 8 = 16 cm.
5. Area = ½ × 12 × 16 = 96 cm²

Check: The four triangles each have area ½ × 6 × 8 = 24 cm², and 4 × 24 = 96 cm². ✔

Answer: The area is 96 cm², which is option D.

Tip: Whenever a rhombus gives you a side and one diagonal, think of the 3-4-5 triple. Here 6-8-10 is just 3-4-5 doubled, so the missing half-diagonal is 8 immediately. Then use Area = ½ × d₁ × d₂.