Triangle Area Calculator
Calculate the area of a triangle given its base and height. Perfect for geometry students, DIY projects, and construction calculations with comprehensive educational content.
Calculate Triangle Area
Enter the base and height of your triangle:
Area = ½ × base × height
Understanding Triangle Area
The area of a triangle is calculated using one of the most fundamental formulas in geometry. By knowing just the base and height of any triangle, you can determine its area using this simple but powerful relationship.
The Triangle Area Formula
📐 Basic Formula
Area = ½ × base × height
This formula works for any triangle
Height must be perpendicular to base
Units must be consistent
🔍 Why It Works
A triangle is half of a parallelogram
The area of a parallelogram is base × height
Therefore triangle area is ½ × base × height
📏 Height Definition
Height is perpendicular distance
From base to opposite vertex
Not necessarily a side of the triangle
Can be inside or outside the triangle
💡 Pro Tip: The height of a triangle is always measured perpendicular to the base. If you don't know which side is the base, you can choose any side as the base and draw the perpendicular height from the opposite vertex.
Common Triangle Examples
| Base | Height | Area | Description |
|---|---|---|---|
| 3 cm | 4 cm | 6 cm² | Basic right triangle |
| 5 cm | 6 cm | 15 cm² | Common classroom example |
| 8 cm | 10 cm | 40 cm² | Larger triangle |
| 12 cm | 15 cm | 90 cm² | Big classroom triangle |
| 10 cm | 8 cm | 40 cm² | Same area, different orientation |
Types of Triangles
📐 Right Triangle
One angle is exactly 90°
Height equals one of the sides
Easiest to calculate area
Pythagorean theorem applies
🔺 Equilateral Triangle
All sides equal length
All angles equal (60° each)
Height = (√3/2) × side
Area = (√3/4) × side²
🔸 Isosceles Triangle
Two sides equal length
Two angles equal
Height may not equal a side
Common in real-world objects
Real-World Applications
🏠 Construction
Roof pitch calculations
Gable end areas
Shed and garage designs
Stair tread calculations
🎨 Design & Art
Geometric pattern design
Canvas area planning
Sculpture calculations
Architectural drafting
🏞️ Landscaping
Garden bed planning
Slope area calculations
Flagstone patio design
Turf area estimation
🏫 Education
Geometry problem solving
Area comparison exercises
Scale model calculations
STEM project planning
Triangle Area Variations
| Method | When to Use | Formula |
|---|---|---|
| Base and Height | Most common method | A = ½ × b × h |
| Two Sides + Angle | When you know an angle | A = ½ × a × b × sin(C) |
| Three Sides | SSS triangle (Heron's formula) | A = √[s(s-a)(s-b)(s-c)] |
| Equilateral | All sides equal | A = (√3/4) × side² |
| Right Triangle | 90° angle present | A = ½ × leg₁ × leg₂ |
Practical Examples
🏠 Roof Section
Roof pitch: 6/12 (rise over run)
Base: 20 feet
Height: 10 feet
Area: 100 square feet
🎄 Christmas Tree
Base: 4 feet
Height: 6 feet
Area: 12 square feet
Skirt area calculation
🏃 Race Flag
Base: 2 feet
Height: 3 feet
Area: 3 square feet
Sports equipment
Common Mistakes to Avoid
- Wrong height: Height must be perpendicular to the base, not slanted
- Mixed units: Base and height must be in the same units
- Wrong base: Any side can be the base, but height must correspond to that base
- Forgetting ½: The formula includes ½, don't forget to divide by 2
- Negative values: Areas cannot be negative - use absolute values
Triangle Area in Different Contexts
📐 Coordinate Geometry
Points: (x₁,y₁), (x₂,y₂), (x³,y³)
Area = ½|x₁(y₂-y³) + x₂(y³-y₁) + x₃(y₁-y₂)|
Shoelace formula method
📏 Trigonometric Method
Two sides and included angle
Area = ½ × a × b × sin(C)
Useful for surveying
🔢 Vector Method
Cross product of vectors
Area = ½ × |u × v|
Advanced mathematical approach