Concept 11.1
Area of a Sector
Source: NCERT Mathematics, Class 108 minute lesson
Formal statement
The area of a sector of angle θ in a circle of radius r is (θ/360) × πr².
The intuition
A sector is a slice of the circle, and θ/360 tells you what fraction of the whole you have. A 90° sector is a quarter, a 60° sector a sixth.
So the formula isn't new: it is the full area πr² times the fraction. Find the fraction first and the rest is multiplication.
The attention
Look at θ/360: it is the share of the circle you have.
Area = θ/360 × πr² not θ × πr²
Look hereNot here
- Look here
- θ/360, the share of the circle. A 60° sector is 60/360 = 1/6 of the circle, so its area is one sixth of πr².
- Not here
- Multiplying by θ itself. Multiplying by θ itself, 60, gives an area 60 times the whole circle. The angle only matters as a share of 360°.
- What it teaches
- Turn a measurement into a fraction of the whole before you calculate.