A rectangle is such that its area is 48 cm² and its perimeter is 28 cm. If a rhombus is formed by joining the midpoints of the si…

Question

A rectangle is such that its area is 48 cm² and its perimeter is 28 cm. If a rhombus is formed by joining the midpoints of the sides of this rectangle, what is the area of the rhombus?

1. A. 12 cm²
2. B. 48 cm²
3. C. 24 cm² (Correct answer)
4. D. 20 cm²

Correct Answer

Option C — 24 cm²

Detailed Solution & Explanation

The correct answer is 24 cm².

Key Points

• Joining the midpoints of any quadrilateral produces a figure of exactly half its area — so the rhombus is half the rectangle.
• The rectangle's area is given as 48 cm², so the rhombus is 48/2 = 24 cm².
• The perimeter is not needed at all, though it is consistent: l + w = 14 and lw = 48 give sides 8 cm and 6 cm.

Additional Information

• The midpoint figure of any quadrilateral is a parallelogram (Varignon's theorem), and its area is always half the original.
• It becomes a rhombus when the original's diagonals are equal — true of a rectangle — and a rectangle when the original's diagonals are perpendicular.
• Check the rhombus directly: its diagonals equal the rectangle's sides, 8 and 6, so area = ½ × d₁ × d₂ = ½ × 8 × 6 = 24 cm² ✓.
• Rhombus area has two forms: ½ × d₁ × d₂ using diagonals, or base × height as for any parallelogram.
• Option B (48) is the trap for anyone who forgets the halving.