Question 35

A rectangle having 10 cm and 6 cm asits dimensions was reconstructed to make a rhombus having the same perimeter as that of the rectangle and 60° as one of its angles. The area of the rhombus, in $$cm^{2}$$, was:

Solution

The correct option is D.

Perimeter of rhombus = perimeter of rectangle = 32cm

Side of rhombus = $$\frac{32}{4}$$ = 8cm

AO = $$cos60^\circ$$ $$\times$$AD = 4cm

DO = $$cos30^\circ\times$$AD= 4$$\sqrt3$$cm

Area of rhombus = $$\frac{1}{2}d_{1}\times d_{2}$$ = $$\frac{1}{2}\times8\times8\sqrt3$$= $$32\sqrt3$$

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