Question

The radius of the circle given above is 7cm and the angle subtended by the arc is ${60}^{\circ }$.
If the area of $\Delta$OAB is $21{cm}^2$, then find the area of segment APBA.
$(\pi =\frac{22}{7})$

• A. $5.8{cm}^2$
• B. $4.7{cm}^2$
• C. $8{cm}^2$
• D. $1{cm}^2$

Answer 1

The correct option is B

$4.7{cm}^2$

$\text{Area of sector OAPBO}=\frac{60°}{360°}\times \pi r^2=\frac{60°}{360°}\times \frac{22}{7}\times 7^2=25.7{cm}^2$

Area of segment APBA
Area of sector OAPBO - Area of triangle OAB
$=25.7-21=4.7{cm}^2$

Therefore, area of segment APBA
$=4.7{cm}^2$