| Method | Inputs | Base (b) | Area (A) | Height (h) |
|---|---|---|---|---|
| Area & Height | A=36, h=9 (cm) | 8 cm | 36 cm² | 9 cm |
| Isosceles | s=10, h=8 (cm) | 12 cm | 48 cm² | 8 cm |
| Coordinates | A(0,0), B(6,0), C(3,4) | 6 cm | 12 cm² | 4 cm |
- General: A = (b × h) / 2 → b = 2A / h
- Isosceles: (b/2)² + h² = s² → b = 2√(s² − h²)
- Coordinates: b = √((x₂−x₁)² + (y₂−y₁)²)
- With third point: area by shoelace, then h = 2A / b
- Select a method that matches your known values.
- Choose your units and preferred decimal precision.
- Fill the required inputs (marked with a red asterisk).
- Press Calculate to show results above the form.
- Use Download CSV or Download PDF to export saved results.
No history yet. Run a calculation to start saving results.
Why base accuracy matters in triangle work
The base is the reference length for area, similarity, scaling, and coordinate geometry. A small base error propagates into area and derived heights, especially when values are later squared or compared across datasets. This calculator displays intermediate steps so you can audit each substitution and keep classroom, lab, or project computations consistent. It supports repeatable practice across worksheets, reports, and assessments today.
Area–height method for fast reconstruction
When area A and perpendicular height h are known, base b follows directly from b = 2A/h. This is efficient for survey sketches, textbook problems, and spreadsheet workflows. Because A and h must be positive, the form validates inputs and prevents division by zero. Adjust the decimals control to match the precision of your measurements.
Isosceles option uses right-triangle splitting
For an isosceles triangle with equal side s and height h, dropping the altitude bisects the base. The relationship (b/2)² + h² = s² gives b = 2√(s² − h²). The calculator checks that h is smaller than s so the square root stays real. The plot highlights symmetry by placing the apex at b/2.
Coordinate inputs support distance and geometry
If you know endpoints A(x1,y1) and B(x2,y2), the base is the Euclidean distance √((x2−x1)²+(y2−y1)²). Adding point C(x3,y3) enables the shoelace area and a computed height to AB using h = 2A/b. This is useful in analytics tasks where points come from maps, sensors, or CAD exports.
Units, rounding, and reporting discipline
Pick a unit once and keep it consistent across all inputs. Area is shown in squared units automatically, reducing notation mistakes. Rounding is presentation-only; internal calculations run with floating-point precision. Use the history table to compare multiple scenarios, then export CSV for further analysis or PDF for submission and documentation.
Practical checks to catch common mistakes
A quick sense-check helps: increasing height while keeping area fixed should decrease the base, and symmetric isosceles inputs should produce a centered apex. For coordinates, confirm the two base points differ and that C is not collinear with AB if you expect nonzero area. The interactive plot makes these checks visible before you export results.
1) What if I only know the base, not the height?
This tool solves for the base. If you already know the base, use A = bh/2 to solve for height when area is known, or provide coordinates to infer height from geometry.
2) Why does the isosceles method require h < s?
Because b = 2√(s² − h²). If h is equal to or larger than s, the expression under the square root becomes zero or negative, which is not a valid triangle.
3) Are coordinate units the same as length units?
Yes. Coordinate differences act like lengths in the chosen unit system. If your points are meters, set units to m; if they are pixels, keep the same interpretation throughout.
4) How is height computed from coordinates with point C?
First, area is computed using the shoelace method. Then height to base AB is h = 2A/b, where b is the distance between A and B. This gives the perpendicular height.
5) Does changing decimals affect saved history?
History saves the formatted values shown at calculation time. If you want the same inputs displayed with different rounding, run the calculation again using a new decimals setting.
6) What does the plot help me verify?
It visualizes the triangle or base segment using your inputs. You can confirm orientation, symmetry, and nonzero area at a glance, which helps catch swapped coordinates or unrealistic dimensions.