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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 12тИЪ3 Correct Answer Incorrect Answer
    B 6 Correct Answer Incorrect Answer
    C 12 Correct Answer Incorrect Answer
    D 9тИЪ3 Correct Answer Incorrect Answer

    Solution

    Let the longest diagonal be d. 42 = 22 + (d/2)2 16 - 4 = d2/4 12 ├Ч 4 = d ├Ч d┬а d = 4тИЪ3 Side of the equilatral triangle = 4тИЪ3 Area of the triangle = (тИЪ3/4) ├Ч a2 = (тИЪ3/4) ├Ч (4тИЪ3) ├Ч (4тИЪ3) Area of the triangle = 12тИЪ3 cm2

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