Purpose and steps
Triangle Calculator validates first side, second side, third side before applying the displayed equation. Area is in squared units; perimeter is in the entered length unit.
- Find a triangle’s area and perimeter from three sides using Heron’s formula. All sides must use the same length unit and satisfy the strict triangle inequality.
- Enter First side, Second side, Third side in the stated format. Baseline values are for reproduction.
- Check the output unit and convention: Read area (heron) with its stated unit and convention. The default example and the independent worked scenario use different inputs, so compare the assumptions before comparing the numbers.
- Change one input and compare the result. Area is in squared units; perimeter is in the entered length unit. Degenerate triangles and zero-length sides are rejected.
Input reference and units
These values reproduce the model’s demonstration. Replace them with your own records or measurements; they are not recommended targets.
On a small screen, swipe the table horizontally to see all columns.
| Parameter | Demonstration value | How to enter it |
|---|---|---|
| First side | 3 | Enter first side without adding a unit suffix. Scope: Area is in squared units; perimeter is in the entered length unit. |
| Second side | 4 | Enter second side without adding a unit suffix. Scope: Area is in squared units; perimeter is in the entered length unit. |
| Third side | 5 | Enter third side without adding a unit suffix. Scope: Area is in squared units; perimeter is in the entered length unit. |
Model-specific method
How this calculator produces its result
Triangle Calculator: s = (a+b+c)/2; area = √(s(s−a)(s−b)(s−c)); perimeter = a+b+c. Input definitions: a = First side; b = Second side; c = Third side. Use the selected convention throughout the calculation.
Triangle Calculator: calculation relationships
Find a triangle’s area and perimeter from three sides using Heron’s formula. All sides must use the same length unit and satisfy the strict triangle inequality. Area is in squared units; perimeter is in the entered length unit. Degenerate triangles and zero-length sides are rejected.
Heron’s formula uses the semi-perimeter. For sides 5, 5 and 6, s=8 and area=√(8×3×3×2)=12 square units; perimeter is 16 length units. An independent check drops the altitude onto half the base: height=√(25−9)=4, and 6×4/2=12. Side feasibility must be checked before taking the square root.
s = (a+b+c)/2; area = √(s(s−a)(s−b)(s−c)); perimeter = a+b+c
- a: First side. Enter first side without adding a unit suffix. Scope: Area is in squared units; perimeter is in the entered length unit.
- b: Second side. Enter second side without adding a unit suffix. Scope: Area is in squared units; perimeter is in the entered length unit.
- c: Third side. Enter third side without adding a unit suffix. Scope: Area is in squared units; perimeter is in the entered length unit.
- Result units: stated beside each output
- Calculation relationship: s = (a+b+c)/2; area = √(s(s−a)(s−b)(s−c)); perimeter = a+b+c
- Supported domain: see the limits below
Worked example
Triangle Calculator baseline input: First side: 3; Second side: 4; Third side: 5. Output: Area (Heron) = 6; Perimeter = 12. Substitute these values into the displayed equation to reproduce the result.
Reproduce the default scenario
This reproduces the default inputs in the reference table above; it is not an additional independent example. Displayed rounding may differ from intermediate precision.
- Area (Heron)
- 6
- Perimeter
- 12
Reading results without overstating them
- Read area (heron) with its stated unit and convention. The default example and the independent worked scenario use different inputs, so compare the assumptions before comparing the numbers.
- Change one input at a time and use the equation to explain the result; do not mix unit, grade-scale, time-zone or rounding conventions across comparisons.
Assumptions and exclusions
- Area is in squared units; perimeter is in the entered length unit.
- Degenerate triangles and zero-length sides are rejected.
Sources and content notes
Toolify describes the implemented algorithm and its assumptions. Sources below support the topic or applicable rules; they do not endorse this calculator. Examples are illustrative, and published rules take precedence over simplified estimates.
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