Calculator
Choose a method, enter the required values, and press calculate. Results appear above this form, directly under the header.
Formula Used
| Method | Formula | Use Case |
|---|---|---|
| Base and Height | A = 1/2 × b × h | Best when the base and perpendicular height are known directly. |
| Heron | A = √[s(s-a)(s-b)(s-c)] | Useful when all three side lengths are known. |
| SAS | A = 1/2 × ab × sin(C) | Helpful when two sides and their included angle are available. |
| Coordinates | A = |x1(y2-y3)+x2(y3-y1)+x3(y1-y2)| / 2 | Ideal for graph, map, and analytic geometry problems. |
| Equilateral | A = (√3 / 4) × a² | Fast option for a triangle with all equal sides. |
This calculator also computes extra metrics whenever enough information exists, including perimeter, semiperimeter, altitude, inradius, circumradius, and triangle classification.
How to Use This Calculator
- Select the triangle input method that matches your known values.
- Enter a unit label such as cm, m, ft, or leave the default text.
- Choose how many decimal places you want in the result.
- Fill only the fields required for your selected method.
- Click Calculate Area to show the result above the form.
- Review the result table, step-by-step working, and the Plotly scaling chart.
- Use the CSV or PDF buttons to export the current result set.
Example Data Table
| Example | Method | Inputs | Area |
|---|---|---|---|
| Example 1 | Base and Height | b = 12, h = 8 | 48 sq units |
| Example 2 | Heron | a = 13, b = 14, c = 15 | 84 sq units |
| Example 3 | SAS | a = 10, b = 9, C = 30° | 22.5 sq units |
| Example 4 | Coordinates | (0,0), (6,0), (2,5) | 15 sq units |
| Example 5 | Equilateral | a = 6 | 15.59 sq units |
FAQs
1. Which method should I choose first?
Choose the method that matches the values you already know. Use base-height for direct dimensions, Heron for three sides, SAS for two sides and an angle, coordinates for graph points, and equilateral for equal-side triangles.
2. Can this calculator handle coordinate geometry problems?
Yes. Enter three points, and the calculator uses the determinant formula to find area. It also estimates side lengths, perimeter, centroid, and other related triangle properties when the points form a valid triangle.
3. Why do I see a triangle inequality error?
That message appears when the three side lengths cannot form a real triangle. The sum of any two sides must always be greater than the third side for a valid triangle.
4. What does the scaling graph mean?
The graph shows how area changes when a similar triangle is resized. If side lengths double, the area becomes four times larger because area scales with the square of the length factor.
5. Does the calculator support radians?
Yes. In the SAS method, you can switch the angle unit between degrees and radians. Internally, the trigonometric calculation uses radians, and the display converts values when needed.
6. Can I export my results?
Yes. The result section includes CSV and PDF download buttons. CSV is useful for spreadsheets, while PDF is helpful for saving, sharing, or printing your computed triangle summary.
7. Are the extra metrics always available?
Not always. Some outputs, such as inradius, circumradius, or classification, require enough information to derive all three sides. Base-height alone cannot determine every triangle property.
8. What units should I enter?
You may use any consistent unit label, such as cm, m, ft, or in. The calculator does not convert units automatically, so all length inputs should use the same measurement system.