The angle round a complete circle is 360.
It takes 60 minutes for the minute hand to competely move round the clock.
If in 20 minutes, the minute hand makes angle θ with the hour hand.
To find θ, we compare the minutes and angle covered by the minute hand to the complete standard minutes and angle. That is,
20/60 = θ/360
1/3 = θ/360
3θ = 360
divide both sides by 3
θ = 120
Thus, in 20 minutes, the minute hand will make angle 120 with the hour hand.
Area of the sector = 1/2 (length of arc x r)
length of arc = θ/360 x 2πr
where r is the radius.
Thus, area of the sector = 1/2 (θ/360 x 2πr x r)
= 1/2 (θ/360 x 2πr2)
= (θ/360 x πr2)
The length of the minute hand represents the radius of the circle.
= 120/360 x π(7)2
but π = 22/7
= 49/3 x 22/7