📐 Area of a Right Triangle Calculator
Calculate the area of a right triangle using different methods
How to Use This Calculator
Choose Calculation Method
Select which measurements you know: base and height, one leg and hypotenuse, or hypotenuse and altitude.
Enter Values
Input the known measurements. Make sure all values are positive numbers.
Calculate
Click "Calculate Area" to compute the area and other triangle properties.
Review Results
See the area, along with calculated side lengths and perimeter (if applicable).
Formula
Method 1: Base and Height
Area = (Base × Height) / 2
Area = (a × b) / 2
Where a and b are the two legs (perpendicular sides) of the right triangle.
Method 2: One Leg and Hypotenuse
Area = (a × √(c² - a²)) / 2
Where a is one leg and c is the hypotenuse. First find the other leg using Pythagorean theorem: b = √(c² - a²), then use Area = (a × b) / 2.
Method 3: Hypotenuse and Altitude
Area = (Hypotenuse × Altitude) / 2
Area = (c × h) / 2
Where c is the hypotenuse and h is the altitude from the right angle to the hypotenuse.
General Formula for Any Triangle:
Area = ½ × base × height
For a right triangle, the base and height are the two perpendicular sides (legs).
About Area of a Right Triangle Calculator
The Area of a Right Triangle Calculator finds the area of a right triangle using different methods depending on what measurements you know. A right triangle has one 90° angle, and its area can be calculated using the two perpendicular sides (legs) as base and height.
When to Use This Calculator
- Geometry: Calculate the area of right triangles in geometric problems
- Construction: Determine material needed for triangular structures
- Education: Learn how to calculate triangle area
- Real Estate: Calculate area of triangular lots or spaces
- Engineering: Design calculations for right triangular components
- Trigonometry: Solve problems involving right triangles
Why Use Our Calculator?
- ✅ Multiple Methods: Calculate area from different known values
- ✅ Accurate Results: Precise calculations using mathematical formulas
- ✅ Complete Information: Shows area and other triangle properties
- ✅ Flexible Input: Works with base/height, leg/hypotenuse, or hypotenuse/altitude
- ✅ Educational: Helps understand area calculation methods
- ✅ Free: No registration required
Key Concepts
- Right Triangle: A triangle with one 90° angle
- Legs: The two sides that form the right angle (perpendicular to each other)
- Hypotenuse: The longest side, opposite the right angle
- Area Formula: Area = ½ × base × height, where base and height are the two legs
- Pythagorean Theorem: a² + b² = c², where a and b are legs and c is hypotenuse
Example
If a right triangle has base = 6 units and height = 8 units:
- Area = (6 × 8) / 2 = 48 / 2 = 24 square units
- Hypotenuse = √(6² + 8²) = √(36 + 64) = √100 = 10 units
- Perimeter = 6 + 8 + 10 = 24 units
Frequently Asked Questions
What is the formula for the area of a right triangle?
The area of a right triangle is (Base × Height) / 2, where base and height are the two perpendicular sides (legs) that form the right angle.
Can I calculate area if I only know the hypotenuse?
No, you need at least one more measurement. You can use: (1) one leg and hypotenuse, (2) hypotenuse and altitude from right angle, or (3) both legs.
What's the difference between base and height in a right triangle?
In a right triangle, the base and height are the two legs (the sides that form the right angle). They are perpendicular to each other. Either leg can be considered the base or height.
Why do we divide by 2 in the area formula?
The formula Area = base × height gives the area of a rectangle. A triangle is half of a rectangle with the same base and height, so we divide by 2.
Can I use the hypotenuse as base or height?
No, for the basic area formula, you need the two perpendicular sides (legs). However, you can calculate area using hypotenuse and altitude: Area = (hypotenuse × altitude) / 2.
Is this formula the same for all triangles?
The formula Area = ½ × base × height works for all triangles. For a right triangle, the base and height are simply the two legs that form the right angle.