📘 Class 9 · Mathematics

Chapter 11: Areas

4 lessons

Areas proves that triangles or parallelograms on the same base and between the same parallels always share equal area, regardless of their exact shape — a tall, narrow triangle and a short, wide one on the identical base can have exactly the same area. This theorem is then applied to area relationships in triangles and quadrilaterals.

1
Introduction to Areas of Plane Figures
Introduction to areas of plane figures.
 2
Exercise 11.1 — Area of Rectangle
Area of rectangle and area of planar regions.
 3
Exercise 11.2 — Parallelograms
Parallelograms on the same base and between the same parallels.
 4
Exercise 11.3 — Triangles
Triangles on the same base and between the same parallels.

A genuine shift in skill

This moves from Class 8's calculation-based area work to proof-based reasoning, extending the congruence proofs from earlier in the syllabus into a new context. Assuming two figures with equal area must also be congruent is a common overreach — they only need to match in area, not shape.