A fan has 3 equally spaced blades. The central dial has an area of 3π cm2. Leng

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A fan has 3 equally spaced blades. The central dial has an area of 3 $π$ cm $^{2}$ . Length of each blade is (20- $\sqrt{3}$ )cm. If a triangle is drawn from the tips of the blades, find its area.

Options:

A . 900 sq cm

B . 300

\sqrt{3}

sq cm

C . 900 sq cm

D . 400

\sqrt{3}

sq units

Answer: Option B
:
B

Ans: b) 300 $\sqrt{2}$ sq cm

Soln: Radius of the dial at the centre: $\sqrt{\frac{3 π}{π}}$

total length of the blade from the centre: (20- $\sqrt{3}$ )+ $\sqrt{3}$ ; = 20.

Half of each side: 30 cos 30. = 10 $\sqrt{3}$ . Total length of each side: 20 $\sqrt{3}$ .

Thus , area: $(\frac{\sqrt{3}}{4}) (20 \sqrt{3})^{2}$ . =300 $\sqrt{2}$ sq cm

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