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?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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