Question

the diagram shows the sector of a circle with centre O and radius 6cm.
MN is a chord of the circle.
Angle MON is 50°.
calculate the area of the shaded segment.
give your answer to three significant figures. optional working out. ​

Answer 1

Answer:

$1.91 {cm}^{2}$

Step-by-step explanation:

Area of the shaded portion = Area of the sector OMN - Area of the triangle OMN =

$\frac{theta}{360} \times \: \pi \: {r}^{2} - \frac{1}{2}ab \sin(theta)$

$= \frac{50}{360} \times 3.14 \times {6}^{2} - ( \frac{1}{2} \times 6 \times 6 \times \sin(50))$

$= 15.70 - 13.79$

$= 1.91 \: {cm}^{2}$