Concept 11.3
Area of a Segment
Source: NCERT Mathematics, Class 1010 minute lesson
Formal statement
Area of the minor segment = area of the corresponding sector − area of the triangle formed by the two radii and the chord.
The intuition
A segment is the region between a chord and its arc. The sector covers it, plus a triangle formed by the two radii.
So remove the triangle: segment = sector − triangle. For r = 14 cm and θ = 90°: 154 − 98 = 56 cm².
The attention
Look at the triangle inside the sector: it has to come out.
Segment = sector − triangle not sector + triangle
Look hereNot here
- Look here
- Subtracting the triangle. The sector includes the triangle OAB. The segment is what's left after removing it.
- Not here
- Adding the triangle. Adding the triangle counts it twice and gives an area bigger than the sector.
- What it teaches
- Find a shape you can compute that contains the one you want, then subtract the extra.