GANITA MANJARI · GRADE 9 · PART I · CHAPTER 6
TRACE — Understanding Perimeter
Think first. Use AI purposefully. Verify always.
DISCOVER
Start with a question.
If you walk once around a rectangle, which lengths do you count? What changes when every side is doubled?
Say what you expect to stay the same and what you expect to change. Then test your prediction in the visual below.
Understand
Perimeter is the total length of a closed boundary, counted once. It is a length, measured in units such as cm or m.
Key Ideas
Area counts square units inside a region; perimeter measures its boundary. Neither alone determines the other.
Visualise
Trace the boundary once. Which lengths repeat?
Method
Identify the actual boundary. List its lengths in one unit. Add them once, and check that you returned to your starting point.
Worked Example
Given
A rectangle has length 8 cm and width 3 cm.
To Find
Find its perimeter.
Formula / Property / Theorem / Reasoning
Opposite sides of a rectangle are equal.
Solution
- P = 8 + 3 + 8 + 3 cm.
- P = 2(8+3) cm.
Result
P = 22 cm. Original AIMS example.
AIMS Method
- A — Attempt independently. Make a prediction or start a sketch.
- I — Investigate the idea. Identify the boundary, region and given conditions.
- M — Make connections. Relate the figure to a known property or rearrangement.
- S — Scrutinise your reasoning. Check conditions, units and whether the result is exact.
Think first. Use AI purposefully. Verify always.
Focused Practice
A rectangle has sides 7 m and 5 m. Find the boundary length and explain why both sides are counted twice.
Check & Feedback
Does doubling all side lengths double or quadruple perimeter?
Textbook connection: Ganita Manjari · Grade 9 · Part I · Chapter 6 · 6.1 · Figures 6.2–6.4 · printed pages 119.