Triangle Area Calculator
Calculate the area of a triangle using base and height or three side lengths with Heron's formula. Supports all triangle types with accurate results.
Result
- Area
- -
Formula & Guide
Formulas
A
Base & Height
Area = ½ × base × height
Multiply base by height, then divide by 2
H
Heron's Formula
Area = √[s(s-a)(s-b)(s-c)]
s = semi-perimeter = (a+b+c)/2
Formula Variables
base
Base
The length of one side of the triangle (usually the bottom side)
height
Height
The perpendicular distance from the base to the opposite vertex
a, b, c
Side Lengths
The three side lengths of the triangle
s
Semi-perimeter
Half the perimeter: s = (a + b + c) / 2
Step-by-Step Scenario
Example Scenario
Base
10 units
Height
6 units
1
Identify the Values
- Base = 10 units, Height = 6 units
Make sure the height is perpendicular to the base
2
Apply the Formula
- Area = ½ × base × height
- Area = ½ × 10 × 6
- Area = ½ × 60
Additional Examples
Right Triangle
Base: 5 units
Height: 4 units
Area
½ × 5 × 4 = 10 square units
Heron's Formula
Sides: 5, 6, 7 units
Semi-perimeter
s = (5+6+7)/2 = 9
Area
√[9(9-5)(9-6)(9-7)] ≈ 14.7
Characteristics of Triangle Area
Multiple Methods
Triangle area can be calculated using base-height method or Heron's formula, providing flexibility based on available information.
Universal Application
Works for all triangle types: equilateral, isosceles, scalene, right, acute, and obtuse triangles.
Practical Uses
Essential for architecture, construction, land surveying, graphic design, and any field involving geometric calculations.
Mathematical Foundation
Triangle area formulas are fundamental to geometry and are used in more complex geometric calculations and proofs.
Important Notes
- The height must be perpendicular to the base. For a right triangle, the two legs can serve as base and height.
- For Heron's formula, the triangle inequality must hold: the sum of any two sides must be greater than the third side.
- The semi-perimeter (s) is always used in Heron's formula and is half the perimeter of the triangle.
- Area is always expressed in square units (e.g., square meters, square feet) based on the units of the input measurements.
- Both methods give the same result for the same triangle, but use different information to calculate it.
Frequently Asked Questions
Find answers to common questions about triangle area calculations.