Why Area of a Triangle Makes Perfect Sense — From Squares to Simplicity
Date: 2025-05-11 • Author: Trafalgar Tuition
📏 Area of a Rectangle — Where It All Begins
Let’s start with something we all know:
\( \text{Area} = \text{base} \times \text{height} \)
This is the foundation of area — and we treat it almost like a postulate (something to be taken; a claim or assumption that is used as a basis for an argument) and this is something we accept as self-evident based on counting unit squares within the shape.
🔺 Now Cut It in Half
If you draw a diagonal line across a rectangle, you split it into two right-angled triangles — each exactly half the area.
\( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \)
Even for non-right-angled triangles, we can drop a perpendicular to create a height — and the logic holds.
✅ This isn’t a rule we memorise. It’s a rule we understand — because it comes from the rectangle.
📐 What About Perimeter?
Perimeter is about distance around a shape, not the area within.
- \( P = 4s \) (square)
- \( P = 2(b + h) \) (rectangle)
- \( P = a + b + c \) (triangle)
| Formula | What it measures | Units used |
|---|---|---|
| Area | Space inside | cm², m², etc. |
| Perimeter | Distance around | cm, m, etc. |
💭 Why This Matters
When you really understand where these formulas come from:
- You don’t just “remember” them
- You can explain them, apply them, and extend them
- You spot when the question wants area vs. perimeter — and why
This is why we created FTSE — Formulae Teachers Should Explain
Because when something makes sense, you don’t forget it.
➡️ Next up: 002 – Trapezium (FTSE002)