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    Question

    In a parallelogram, the lengths of the diagonals are 24

    cm and 10 cm, and the angle between the diagonals is 30°. Find the area of the parallelogram.
    A 42 cm² Correct Answer Incorrect Answer
    B 32 cm² Correct Answer Incorrect Answer
    C 60 cm² Correct Answer Incorrect Answer
    D 55 cm² Correct Answer Incorrect Answer

    Solution

    Area of a parallelogram in terms of diagonals d₁, d₂ and angle θ between them: Area = (1/2) d₁ d₂ sinθ Here d₁ = 24, d₂ = 10, θ = 30°. Area = (1/2) × 24 × 10 × sin 30° = 12 × 10 × (1/2) = 60 cm²

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