NECO 2005 Mathematics · Question 36

The diagonals of a rhombus are 6cm and 8cm. Find the area of the rhombus.

Options

A.96cm2
B.48cm2
C.24cm2
D.0.14cm2
E.12cm2

Answer: C. 24cm2

Explanation written with AI and checked against the answer key

Analyze the question: We're given the two diagonals of a rhombus (6 cm and 8 cm) and asked for 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 formula using diagonals is: Area = ½ × d₁ × d₂ Solution: Area = ½ × 6 × 8 Area = ½ × 48 Area = 24 cm² Check using triangles: Each half-diagonal is 3 cm and 4 cm, so each right triangle has area ½ × 3 × 4 = 6 cm². Four triangles give 4 × 6 = 24 cm². (The side of the rhombus is √(3² + 4²) = 5 cm, a nice 3-4-5 triangle.) Tip: Do not forget the ½. If you multiply the diagonals only (6 × 8 = 48), you land on option B, a common trap. The same ½ × d₁ × d₂ formula works for a kite too.

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