Question

In the figure given below, the radius of the circle is 42cm. The angle in the sector is ${60}^{\circ }$​. What is the area of the segment APB?

• A. $924sqcm$
• B. $441\sqrt{3}sqcm$
• C. $924-441\sqrt{3}sqcm$
• D. $1743sqcm$

Answer 1

The correct option is C $924-441\sqrt{3}sqcm$

Area of segment APB = Area of sector OAPB - Area of $△$OAB
Area of segment OAPB = $\frac{60}{360}\times \pi \times {42}^2=924sq.cm$
Now Area of $△$OAB = $\frac{\sqrt{3}}{4}\times r^2=\frac{\sqrt{3}}{4}\times 42\times 42=441\sqrt{3}sqcm$
Hence, area of segment APB = Area of sector OAPB -Area of $△$OAB $=924-441\sqrt{3}sqcm.$