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The smaller diagonal of a rhombus is equal to the length of its sides. If the length of each side is 4 cm, then what is the area (in cm2) of an equilateral triangle with side equal to the bigger diagonal of the rhombus?

The smaller diagonal of a rhombus is equal to the length of its sides. If the length of each side is 4 cm, then what is the area (in cm2) of an equilateral triangle with side equal to the bigger diagonal of the rhombus? Correct Answer 12√3

Let ABCD be the given rhombus and AC be the bigger diagonal.

So, AB = BD = 4 cm

So, ΔABD is an equilateral triangle

⇒ Ar (ΔABD) = √3 (side)2/4

⇒ Ar (ΔABD) = 4√3

Now, Ar (rhombus ABCD) = 2

⇒ Ar (rhombus ABCD) = 8√3

Also, Ar (rhombus ABCD) = ( 1/2) × AC ×BD

⇒ (1/2) × AC × BD = 8√3

⇒ AC = (8√3 × 2)/4 = 4√3

Now, AC is the side of new equilateral Δ

⇒ Area of new triangle = /4

⇒ Required area = 12√3 cm2

∴ the correct option is 4) 

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