Question

A fan has 3 equally spaced blades. The central dial has an area of 3$\pi$ 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.

• A. 900 sq cm
• B. 300$\sqrt{3}$ sq cm
• C. 900 sq cm
• D. 400$\sqrt{3}$ sq units

Answer 1

The correct option is B

300$\sqrt{3}$ sq cm

Radius of the dial at the centre = $\sqrt{3}$

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

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

Total length of each side: $20\sqrt{3}$

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