Triangle Area Calculator
Area of a triangle from its base and height.
Area
30
½ × 10 × 6
Base × Height
60
AI Breakdown & Smart Takeaway
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How the Triangle Area Calculator works
The Triangle Area Calculator instantly computes the area of any triangle when you know its base and height, making it an essential tool for students, architects, engineers, landscapers, and anyone working with triangular shapes in real-world geometry problems.
At its core, this calculator applies the foundational geometry formula for triangle area: one-half times the base multiplied by the height. You simply enter two measurements — the length of the base and the perpendicular height — and the calculator returns the area in the same square units you used for input. This works for every triangle type, whether it's equilateral, isosceles, scalene, right-angled, or obtuse, because the formula is universally valid regardless of triangle shape.
The key insight behind the formula is that a triangle is exactly half of a parallelogram with the same base and height. Imagine completing your triangle into a rectangle or parallelogram: the triangle always occupies precisely half that area. This is why the factor of one-half appears in the formula and why the height must be the perpendicular height — the straight-line distance from the base to the opposite vertex measured at a right angle — not the length of a slanted side.
One of the most common mistakes users make is confusing the slant side length with the perpendicular height. In a right triangle, this distinction disappears on the side adjacent to the right angle, but in obtuse or scalene triangles, the height may even fall outside the triangle itself (an external altitude). Always verify you are measuring the true perpendicular drop from the apex to the base line, extended if necessary. Entering a slant side instead of the true height will overestimate the area, sometimes significantly.
In practical applications — such as calculating the area of a triangular garden plot, a roof gable, a sail, or a land parcel — you will often need to convert your measurements into consistent units before entering them. If your base is in feet and your height is in inches, convert both to the same unit first. The calculator returns area in square units (e.g., square feet, square meters, square centimeters), so scaling matters. For large civil engineering or surveying projects, working in meters and converting to square meters or hectares afterward is standard practice.
Formula
Area = ½ × base × height
Pro tips
- Always confirm your height is truly perpendicular to the base — use a square or verify a 90° angle in your diagram before entering values, as even small angular errors cause meaningful area errors.
- You can choose any of the three sides as the base; pick whichever side you have the corresponding perpendicular height for, since all three base-height pairs will yield the same area.
- For real-world measurements like land or roofing, measure in one consistent unit throughout (all feet or all meters) and only convert the final area result to avoid compounding rounding errors.
- If you only know all three side lengths but not the height, use Heron's Formula instead: first calculate the semi-perimeter s = (a+b+c)/2, then Area = √(s(s−a)(s−b)(s−c)).
- When working with obtuse triangles, remember the altitude from the obtuse vertex falls outside the triangle — extend the base line and measure perpendicularly from that extension point to the vertex.
Key terms
- Base
- — Any one side of the triangle chosen as the reference side from which the perpendicular height is measured.
- Perpendicular Height (Altitude)
- — The straight-line distance measured at exactly 90° from the base to the opposite vertex, which may fall outside the triangle for obtuse triangles.
- Triangle Area
- — The total two-dimensional space enclosed within the three sides of a triangle, expressed in square units.
- Square Units
- — The unit of measurement for area, representing a 1×1 square in whatever linear unit was used (e.g., square meters, square feet, square centimeters).
- Altitude
- — Another term for the perpendicular height of a triangle; every triangle has three possible altitudes, one from each vertex to its opposite side.
- Scalene Triangle
- — A triangle in which all three sides and all three angles are different, requiring careful identification of the correct perpendicular height for each chosen base.