1.

1). 62). 9√33). 124). 12√3

Answer»

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 (ΔABD)]

⇒ 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 = [√3 × (4√3)2]/4

REQUIRED area = 12√3 cm2

∴ the correct option is 4) 



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