Rhombus with diagonals in 0.8 ratio — area relative to longer diagonal squared: In a rhombus, one diagonal is 80% of the other. The area equals what fraction of the square of the longer diagonal?

Introduction / Context:For a rhombus, area = (d1 * d2) / 2. A ratio between diagonals enables expressing the area as a fraction of the longer diagonal squared.

Given Data / Assumptions:

• Let longer diagonal = D
• Shorter diagonal = 0.8D

Concept / Approach:Area A = (D * 0.8D) / 2 = 0.4 * D^2. Thus the area is 2/5 of the square of the longer diagonal.

Step-by-Step Solution:A = (D * 0.8D)/2 = 0.4 D^2 = 2/5 * D^2

Verification / Alternative check:Setting D = 10 gives A = 20; scaling D^2 by 2/5 matches.

Why Other Options Are Wrong:4/5 and 3/4 are too large; 1/4 ignores the 0.8 factor.

Common Pitfalls:Forgetting the division by 2 in the rhombus area formula.

Final Answer:2/5