Triangle Area Calculator
Choose a method, enter your values, and instantly calculate the area of a triangle.
What This Triangle Area Calculator Does
This calculator helps you quickly find the area of a triangle using three common methods: base and height, three side lengths, and coordinate points. It is useful for school math, geometry homework, construction layouts, CAD drafts, and everyday measurements.
If you already know the base and height, use the simplest method. If only the sides are known, Heron's formula is ideal. If your triangle is plotted on a graph, coordinate mode is usually the fastest route.
Triangle Area Formulas
1) Base and Height Formula
The most common formula is:
Area = (1/2) × base × height
- Base can be any side of the triangle.
- Height must be perpendicular to that base.
- Both values should use the same unit.
2) Heron's Formula (When You Know 3 Sides)
If you know side lengths a, b, and c, use:
s = (a + b + c) / 2 (semi-perimeter)
Area = √(s(s-a)(s-b)(s-c))
This method is especially helpful when no altitude is provided.
3) Coordinate Geometry Formula
For points (x₁,y₁), (x₂,y₂), and (x₃,y₃):
Area = |x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)| / 2
This is perfect for graph-based problems and digital plotting.
Worked Examples
Example A: Base and Height
Base = 12 cm, Height = 7 cm
Area = (1/2) × 12 × 7 = 42 cm²
Example B: Three Sides
a = 6, b = 8, c = 10
s = (6 + 8 + 10) / 2 = 12
Area = √(12×6×4×2) = √576 = 24 square units
Example C: Coordinates
(0,0), (4,0), (1,3)
Area = |0(0−3) + 4(3−0) + 1(0−0)| / 2 = |12|/2 = 6 square units
Common Mistakes to Avoid
- Using side length as height when the height is not perpendicular.
- Mixing units (for example, meters and centimeters in one formula).
- Using invalid side lengths that cannot form a triangle (fails triangle inequality).
- Ignoring that area is always in squared units (cm², m², in²).
Where You Might Use This in Real Life
- Estimating triangular floor, roof, or panel coverage
- Land surveying and map reading
- Engineering sketches and 2D model calculations
- Math test prep and classroom exercises
Quick FAQ
Can area ever be negative?
No. Area is always zero or positive. If you get zero, your points may be collinear or dimensions may be invalid.
What if I only know two sides?
You need more information (an included angle, a height, or the third side) to calculate area uniquely.
Does this calculator support decimals?
Yes. You can enter integers or decimal values in all numeric fields.