A kite in the shape of a square with a diagonal 32 cm attached to an equilateral triangle of the base cm. Approximately how much paper has been used to make it?

A kite in the shape of a square with a diagonal 32 cm attached to an equilateral triangle of the base 8 cm. Approximately how much paper has been used to make it?
[A]539.217 cm^{2}
[B]538.721 cm^{2}
[C]540.712 cm^{2}
[D]539.712 cm^{2}

539.712 cm^{2}
Area of paper = Area of square + Area of equilateral triangle
= \frac{1}{2}(diagonal)^{2} + \frac{\sqrt{3}}{4}\times (side)^{2}
= \frac{1}{2}\times 32 \times 32 + \frac{\sqrt{3}}{4}\times8 \times 8
= 512 + 16 \times 1.732
= 512 +27.712 = 539.712 cm^{2} [∴ Diagonal of a square = \sqrt{2} \times side]
Hence option [D] is the right answer.

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