Question

Find the area of the shaded region in PQRSPQRS is an equilateral triangle

• A. $(6\pi -9\sqrt{3})c{m}^2$
• B. $(4\pi -9\sqrt{3})c{m}^2$
• C. $(3\pi -9\sqrt{3})c{m}^2$
• D. $(2\pi -9\sqrt{3})c{m}^2$
• E. None of these

Answer 1

The correct option is A $(6\pi -9\sqrt{3})c{m}^2$

Area of segment $=\frac{Q-\sin \theta }{2}\times r^2$

$=\frac{\frac{\pi }{3}-\sin \frac{\pi }{3}}{2}\times r^2$

$=\frac{\frac{\pi }{3}-\frac{\sqrt{3}}{2}}{2}\times 3b$

$=\frac{2\pi -3\sqrt{3}}{12}\times 3bc{m}^2$ unit

$=(6\pi -9\sqrt{3})c{m}^2$ unit