GANITA MANJARI · GRADE 9 · PART I · CHAPTER 6
RESHAPE — Rectangle and Parallelogram Area
Think first. Use AI purposefully. Verify always.
DISCOVER
Start with a question.
If a parallelogram is sheared sideways while base and height stay fixed, does its area change?
Say what you expect to stay the same and what you expect to change. Then test your prediction in the visual below.
Understand
Rectangle area is ab. A parallelogram can be cut and rearranged to a rectangle with the same base and perpendicular height; its area is bh.
Key Ideas
The sloping side is usually not the perpendicular height. Keeping side lengths fixed does not fix parallelogram area.
Visualise
Move the top edge without changing base or perpendicular height.
Area stays constant. The sloping side and perimeter may change.
Method
Choose a base, identify its perpendicular height, then multiply. For a thin parallelogram, repeated finite cuts can move the overhang before forming a rectangle.
Worked Example
Given
A parallelogram has base 9 cm and perpendicular height 4 cm.
To Find
Find its area.
Formula / Property / Theorem / Reasoning
Area = base × perpendicular height.
Solution
- A = 9 × 4 .
- A horizontal shear keeps this base and height unchanged.
Result
36 . 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
Two parallelograms each have base 8 cm; their perpendicular heights are 3 cm and 5 cm. Compare their areas.
Check & Feedback
What happens to area when only the horizontal shear changes?
Textbook connection: Ganita Manjari · Grade 9 · Part I · Chapter 6 · 6.6–6.7 · Figures 6.16–6.19 · printed pages 130–132.