Question

In the figure, A (O-AXB) is 75.36 cm² and radius is 12 cm, find the area of the segment AXB. ($\mathrm{\pi }$ = 3.14, $\sqrt{3}=1.73).$

Answer 1

Given:
Area of sector O-AXB = 75.36 cm²
Radius, r = 12 cm
Now,
ar($∆$OAB) = $\frac{1}{2}\times r^2\times \mathrm{sin\theta }$
= $\frac{1}{2}\times {12}^2\times \sin 60°$
= $72\times \frac{\sqrt{3}}{2}$
= 36 × 1.73
= 62.28 cm²
Thus, we have:
Area of segment AXB = Area of sector O-AXB $-$ Area of $∆$OAB
= 75.36 cm² $-$ 62.28 cm²
= 13.08 cm²