🗺️ Chapter Roadmap
1 Basic Differences
Mensuration is the branch of math that deals with measuring lengths, areas, and volumes. Before we learn formulas, you must understand what we are actually measuring:
Perimeter
The total length of the outer boundary. Think of it as the length of a fence around a park.
Unit: m, cm, kmArea
The amount of flat surface covered by a shape. Think of it as the tiles on a floor.
Volume
The 3D space occupied by an object. Think of the amount of water inside a tank.
2 2D Shapes (Area & Perimeter)
2D shapes are flat. These formulas are the "bread and butter" of geometry exams.
| Shape | Perimeter (Boundary) | Area (Surface) |
|---|---|---|
| RectangleLength (L), Width (W) | 2(L + W) | L × W |
| SquareSide (s) | 4 × s | s2 |
| TriangleBase (b), Height (h) | Sum of 3 sides |
12
× b × h
|
3 The Magic of Pi (π)
Whenever you deal with a round shape, the number π (Pi) will always be there. Pi is approximately 3.14159 or 22/7.
Circumference (Perimeter)
(2 × 3.14 × Radius)
Circle Area
(3.14 × Radius × Radius)
4 3D Shapes (Volume)
Volume tells us how much "stuff" (like water or air) can fit inside an object. Volume is always measured in Cubic units (cm3, m3).
Cube
A box where all sides are equal. Like a dice.
Cylinder
Like a can of soda or a water pipe. It has height (h) and a circular base (r).
5 Exam Word Problems (Cost Trick)
Examiners don't just ask for Area; they often ask for the Cost of doing something. Here is the secret to never getting these wrong:
🧱 Fencing Problems
When the question asks for the cost of fencing, bordering, or putting a boundary wall...
Use PERIMETER
🧹 Carpeting Problems
When the question asks for the cost of carpeting, painting, tiling, or plowing a field...
Use AREA
📝 Solved Example:
Find the cost of carpeting a room 10m long and 8m wide if the carpet costs $10 per square meter.