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    Question

    The altitude of an equilateral triangle is 6√3 cm.

    Find the area of the equilateral triangle.
    A 30√3 sq cm Correct Answer Incorrect Answer
    B 12√3 sq cm Correct Answer Incorrect Answer
    C 18√3 sq cm Correct Answer Incorrect Answer
    D 36√3 sq cm Correct Answer Incorrect Answer

    Solution

    Let each side of the equilateral triangle be ‘a’ cm

    Therefore, (a 2  – a 2 /4) = (6√3) 2

    Or, 3a 2 /4 = 108

    Or, a 2  = 144

    Or, a = 12 cm

    Therefore, area of the equilateral triangle = √3a 2 /4

    Or, area of the equilateral triangle = (√3 × 144)/4 = 36√3 cm 2

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