Rectangle with diagonal 6 cm, diagonal makes 30° with a side — area In a rectangle, the diagonal has length 6 cm and makes a 30° angle with one side. Find the area of the rectangle.

Introduction / Context:
Knowing the diagonal and its angle with a side determines both side lengths via basic trigonometry, from which the area follows directly.

Given Data / Assumptions:

• Diagonal d = 6 cm.
• Let sides be a (adjacent to the 30°) and b (opposite).
• Angle between diagonal and side a = 30°.

Concept / Approach:
tan 30° = b/a = 1/√3 ⇒ b = a/√3. Also, d² = a² + b². Substitute b and solve for a, then compute area A = a·b.

Step-by-Step Solution:

Verification / Alternative check:
Compute diagonal from a and b: √(27 + 9) = √36 = 6 (consistent).

Why Other Options Are Wrong:
9 cm² corresponds to b = 3 with a = 3, which would make tan 30° = 1; 27 and 36 cm² are incompatible with d = 6.

Common Pitfalls:
Using sin or cos instead of tan to relate a and b at the specified angle.

Final Answer:
9 √3 cm2