Find a triangle's area and perimeter from three sides (Heron's formula) or from base and height.
Enter your values and click Calculate to see the result.
This free triangular calculator finds a triangle's area and perimeter from whichever measurements you already have — all three side lengths, using the classical Heron's formula, or a base and its perpendicular height, using the simplest area formula in geometry. Both methods are exact, not approximations, and this tool shows the full substitution behind either one. Whether you're checking a geometry homework answer, estimating a triangular plot of land, or calculating material for a triangular panel, this triangular calculator gives you the area and perimeter instantly.
A triangle's area can be found two different ways depending on what you know: Heron's formula uses only the three side lengths (no angle or height needed at all), while the base-height formula uses a base and the perpendicular distance to the opposite vertex. This calculator implements both, letting you pick whichever matches your available measurements.
Students and teachers checking geometry homework, surveyors estimating triangular land plots, contractors calculating material for triangular panels or gables, and anyone who has some triangle measurements and needs the area or perimeter quickly can use this tool.
The triangle is the simplest possible polygon, and its area formula underlies the area calculations for every other polygon — any polygon can be split into triangles, and its total area found by summing each triangle's area. Being able to compute a triangle's area reliably from whichever measurements are available is therefore a foundational geometry skill.
Surveyors calculate the area of triangular land parcels from three measured boundary lengths. Architects and roofers compute the area of triangular gable ends or roof sections from base and rise measurements. Students verify textbook geometry problems. Manufacturers estimate material needed for triangular panels, signs, or sails.
Two exact methods, depending on what you know
Given only three side lengths, Heron's formula computes the exact area with no angle or height measurement needed.
Every triangle's area can be found as half its base times its perpendicular height, regardless of the triangle's shape.
You can choose any of the three sides as the "base" — just make sure the height you use is perpendicular to that specific side.
From choosing a mode to reading the result
Pick "Three Sides" if you know all three side lengths, or "Base & Height" if you know the base and perpendicular height.
Type in the three sides, or the base and height, depending on your mode.
The calculator applies Heron's formula or the base-height formula automatically.
Review the computed area, and perimeter when three sides were entered.
Cross-check using the alternative method if you have enough information for both.
Finding the area of a triangular plot with sides 5, 6, and 7
A triangular plot of land has sides measuring 5, 6, and 7 units. Find its area and perimeter.
Explanation: The triangle's area is approximately 14.697 square units, found without ever needing to know any of its angles. If instead you knew this triangle had a base of 7.48 units and a height of 3.93 units relative to that base, the base-height formula would give the same area: ½×7.48×3.93≈14.697 — confirming both methods agree.
What each output field represents
| Field | What It Means |
|---|---|
| Area | The two-dimensional space enclosed by the triangle, in squared units |
| Perimeter | The total distance around all three sides (Three Sides mode only) |
| Semi-perimeter | Half the perimeter, an intermediate value used by Heron's formula |
Manual verification: if you know both the three sides and the height relative to one of them, compute the area both ways (Heron's and base-height) and confirm they match — a strong sanity check on your measurements.
Where finding a triangle's area or perimeter quickly is useful
Check triangle area and perimeter problems step by step.
Estimate the area of a triangular plot from measured boundary lengths.
Calculate the area of a triangular gable end or roof section.
Estimate material needed for triangular signs or panels.
Calculate the area of a triangular sail from its dimensions.
Find fabric area needed for triangular pattern pieces.
Verify triangular component area matches design specifications.
Estimate the area of an irregular triangular field section.
Compute triangular floor or facade element areas.
Compute individual triangle areas in a 3D polygon mesh.
Calculate triangular tile piece area for material estimates.
Practice triangle area problems common in geometry exams.
What this triangular calculator does well, and where it doesn't apply
Two exact methods for the same quantity
| Method | Requires | Also Gives Perimeter? |
|---|---|---|
| Heron's Formula | All three side lengths | Yes |
| Base & Height | One base + its perpendicular height | No |
Summary: This triangular calculator gives you an instant, free way to find a triangle's area and perimeter — from three sides using Heron's formula, or from base and height — with the working shown. Pair it with the Triangle Solver and Right Angle Triangle Calculator for angle-solving and right-triangle-specific needs.
Common questions about triangle area and perimeter
Trusted educational references to go deeper on triangle area
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