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    Question

    Smaller diagonal of a rhombus is equal to length of its

    sides. If length of each side is 4 cm, then what is the area (in square cm) of an equilateral triangle with side equal to the bigger diagonal of the rhombus?
    A 12√3 Correct Answer Incorrect Answer
    B 6 Correct Answer Incorrect Answer
    C 12 Correct Answer Incorrect Answer
    D 9√3 Correct Answer Incorrect Answer

    Solution

    Let the longest diagonal be d. 42 = 22 + (d/2)2 16 - 4 = d2/4 12 × 4 = d × d  d = 4√3 Side of the equilatral triangle = 4√3 Area of the triangle = (√3/4) × a2 = (√3/4) × (4√3) × (4√3) Area of the triangle = 12√3 cm2

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