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.

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Solve this multiple-choice question and choose the correct option.

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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: b = a/√3d² = a² + b² = a² + a²/3 = (4/3)a²6² = (4/3)a² ⇒ a² = 27 ⇒ a = 3√3, b = 3Area A = a·b = 3√3 · 3 = 9√3 cm² 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

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.

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