Question

In the given figure, the centre of the circle is A and ABCDEF is a regular hexagon of side 6 cm, then find the area of segment $BPF$ $(\sqrt{3}=1.73,\pi =3.14)$.

• A. $22.11c{m}^2$
• B. $11.22c{m}^2$
• C. $21.12c{m}^2$
• D. $12.21c{m}^2$

Answer 1

The correct option is A $22.11c{m}^2$

Radius $=AB=6$ cm

Angle at the centre $\angle BFA={120}^0$

Area of section $BPF=$ Area of $△BPF$

$=$ Area of $△ABF$

$=\frac{22}{7}\times 6^2\left(\frac{120}{360}\right)-\frac{\sqrt{3}}{4}\times (6{)}^2$

$=\left(\frac{264}{7}\right)-15.57$

$=\frac{264-108.99}{7}$

$=\frac{155.01}{7}$

$=22.14{cm}^2\approx 22.11{cm}^2$