A “half triangle” usually refers to a right-angled triangle, especially one that is formed by splitting a rectangle or square in half diagonally. Let’s break down the concept of half triangle area, understand how to compute it, and present it through formulas, examples, and tables.
Half Triangle Area Calculator
✅ What is a Half Triangle?
A half triangle can typically be seen as:
- A right-angled triangle formed when a rectangle is divided diagonally.
- A triangle with base and height, where the area is exactly half of a rectangle having the same dimensions.
Visual Example:
If you cut a rectangle of 6 cm × 4 cm diagonally, you get two right-angled triangles:
- Base = 6 cm
- Height = 4 cm
- Area of each triangle = ½ × base × height = 12 cm²
📏 Formula for Area of a Half Triangle
Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}Area=21×base×height
Where:
- Base (b) = the length of the triangle's base
- Height (h) = the perpendicular height from the base
📘 Table 1: Area of Half Triangle for Common Base & Height Values
| Base (b) | Height (h) | Area = ½ × b × h |
|---|---|---|
| 2 cm | 4 cm | 4 cm² |
| 3 cm | 6 cm | 9 cm² |
| 5 cm | 10 cm | 25 cm² |
| 6 cm | 8 cm | 24 cm² |
| 7 cm | 14 cm | 49 cm² |
| 10 cm | 5 cm | 25 cm² |
| 12 cm | 10 cm | 60 cm² |
🧮 Step-by-Step Example
Let’s say we have a triangle with:
- Base = 8 cm
- Height = 5 cm
Step 1:
Use the formula Area=12×8×5=20 cm2\text{Area} = \frac{1}{2} \times 8 \times 5 = 20 \text{ cm}^2Area=21×8×5=20 cm2
📊 Table 2: Area Comparison with Full Rectangle
| Rectangle Dimensions | Triangle Base | Triangle Height | Full Rectangle Area | Half Triangle Area |
|---|---|---|---|---|
| 4 × 6 | 4 | 6 | 24 cm² | 12 cm² |
| 10 × 8 | 10 | 8 | 80 cm² | 40 cm² |
| 12 × 3 | 12 | 3 | 36 cm² | 18 cm² |
| 14 × 7 | 14 | 7 | 98 cm² | 49 cm² |
📘 Table 4: Solve for Missing Value
| Known Area | Known Base | Missing Height |
|---|---|---|
| 20 cm² | 4 cm | 10 cm |
| 18 cm² | 6 cm | 6 cm |
| 30 cm² | 5 cm | 12 cm |
| Known Area | Known Height | Missing Base |
|---|---|---|
| 12 cm² | 4 cm | 6 cm |
| 24 cm² | 6 cm | 8 cm |
| 40 cm² | 10 cm | 8 cm |
🧠 FAQs About Half Triangle Area
❓Is "half triangle" a standard term?
No, it's more of a visual description. In geometry, it's just a right triangle or triangle with base and height.
❓Does the triangle have to be right-angled?
No, but right-angled triangles often result from halving rectangles.
❓Can you use Heron’s formula?
Yes, for non-right triangles where base and height aren’t known, use Heron’s formula.
📌 Summary Table: Half Triangle Area Essentials
| Topic | Summary |
|---|---|
| Definition | A triangle formed by halving a rectangle or triangle with base & height |
| Formula | Area = ½ × base × height |
| Units | Always in square units |
| Useful for | Right triangles, geometry, architecture, construction |
| Key use | Calculating areas of triangular plots, sails, supports, etc. |