Triangle Area Calculator
Calculate the area of a triangle using base and height.
Enter Triangle Dimensions
Table of Contents
Understanding Triangle Area
The area of a triangle is one of the most fundamental concepts in geometry, representing the space enclosed by three straight lines forming the triangle's sides. Understanding how to calculate the area of triangles is essential in fields like architecture, engineering, computer graphics, and mathematics.
Multiple Methods for Calculating Triangle Area
Base-Height Method
The most common and straightforward method uses the triangle's base and height:
Area = (1/2) × base × height
This formula works for all triangles regardless of their type. The height must be measured perpendicular to the base.
Heron's Formula (Three Sides Method)
When you know all three sides of a triangle but don't have height information, Heron's formula is extremely useful:
s = (a + b + c)/2 (semi-perimeter)
Area = √[s(s-a)(s-b)(s-c)]
This formula, attributed to Hero of Alexandria, works for any triangle when you know the lengths of all three sides.
Trigonometric Methods
Using trigonometry, you can calculate the area when you know:
- Two sides and the included angle (SAS method):
Area = (1/2) × a × b × sin(C)
- Three angles and one side (using the Law of Sines)
- Two sides and one non-included angle
Area Formulas for Special Triangles
Equilateral Triangle
When all sides have equal length:
Area = (√3/4) × side²
Right Triangle
When one angle is 90 degrees:
Area = (1/2) × leg1 × leg2
This is simply half the area of a rectangle with the same dimensions.
Isosceles Triangle
When two sides have equal length:
Area = (1/4) × b × √(4a² - b²)
Where a represents the equal sides and b is the third side.
Applications in Real Life
Triangle area calculations have numerous practical applications:
- Architecture: Calculating roofing materials needed for triangular sections
- Land Surveying: Determining property areas with irregular boundaries
- Engineering: Structural analysis and design
- Computer Graphics: Rendering triangulated surfaces in 3D modeling
- Navigation: Finding distances using triangulation
Whether you're a student learning basic geometry, an architect designing a roof, or a computer programmer working on graphics, understanding how to calculate the area of triangles provides a powerful tool for solving real-world problems.
What is Area?
The area of a triangle is the amount of space enclosed within its three sides. It's measured in square units and represents the two-dimensional space that the triangle occupies.
Triangle Area Formula
Formula
A = (1/2) × b × h
where b is the base and h is the height
How to Calculate Triangle Area
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1Measure the base of the triangle
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2Measure the height of the triangle
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3Multiply the base by the height
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4Divide the result by 2
Practical Examples
Example
A triangle has a base of 6 units and a height of 4 units.
A = (1/2) × b × h
A = (1/2) × 6 × 4
A = (1/2) × 24
A = 12 square units