1
Understand perimeter
Measure boundary length of polygons and curved shapes.
Chapter route
Mensuration: Area and Perimeter
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2
Find perimeter of joined shapes
Add required side lengths while avoiding internal boundaries.
3
Understand pi
Connect the circumference of any circle to its diameter.
4
Use approximations of π
Compare approximate values from Archimedes, Aryabhata and Zu Chongzhi.
5
Find circle boundary length
Use radius or diameter to compute circumference.
6
Find arc length
Use fraction of circumference based on central angle.
7
Find rectangle area
Use length and breadth to calculate area.
8
Find parallelogram area
Use base and height to determine area.
9
Find triangle area
Use half of base times height.
10
Median makes equal areas
Use same base or equal base and common height reasoning.
11
Use Heron’s formula
Calculate area from three side lengths using semi-perimeter.
12
Can Heron be used?
Verify triangle possibility before using side-length area formula.
13
What is squaring a shape?
Understand the idea of constructing a square equal in area to a given shape.
14
Square a rectangle historically
Connect ancient geometric construction with area preservation.
15
Why area of circle works
Understand the area formula through visual reasoning.
16
Find circle area
Use radius to compute circular area.
17
Find sector area
Use central angle as a fraction of full circle area.
18
Find segment area
Subtract triangle area from sector area where appropriate.
19
Know Brahmagupta’s formula
Recognise the formula for area of a cyclic quadrilateral from its sides.
20
Find cyclic 4-gon area
Apply the formula when four sides of a cyclic quadrilateral are known.
21
Connect Heron and Brahmagupta
Understand special case and generalisation through area formulae.
22
Use mensuration in real life
Apply formulas to fencing, flooring, circular tracks and designs.
23
Split shapes for area
Decompose complex figures and combine known areas systematically.
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