Question

The perimeter of a rhombus is 40 cm and the length of one of the diagonals of the rhombus is 16 cm. What would be the area of the rhombus?

• A. 40 sq. cm
• B. 64 sq. cm
• C. 96 sq. cm
• D. 100 sq. cm

Answer 1

The Correct Option is C

Calculating the Area of a Rhombus

Step 1: Formula for the Area of a Rhombus 

The area A of a rhombus is given by:

Area = (1/2) × d₁ × d₂

where d₁ and d₂ are the diagonals.

Step 2: Finding the Side Length

The perimeter of the rhombus is 40 cm, so the length of each side is:

Side length = 40 / 4 = 10 cm

Step 3: Using the Pythagorean Theorem

One diagonal is given as d₁ = 16 cm. Since the diagonals bisect each other at right angles, each half-diagonal forms a right-angled triangle with the side of the rhombus.

Applying the Pythagorean theorem:

(d₁ / 2)² + (d₂ / 2)² = Side²

Substituting d₁ = 16 and Side = 10:

(16 / 2)² + (d₂ / 2)² = 10²

8² + (d₂ / 2)² = 100

64 + (d₂ / 2)² = 100

(d₂ / 2)² = 36 ⇒ d₂ / 2 = 6

d₂ = 12 cm

Step 4: Calculating the Area

Area = (1/2) × 16 × 12

= 96 sq. cm

Final Answer:

Thus, the correct answer is (C) 96 sq. cm.