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What Is the Semi-Perimeter?

Definition, formula, examples, and triangle relationships for semi-perimeter in Heron's formula.

What Is the Semi-Perimeter?

Quick Answer

Semi-perimeter is half the triangle perimeter.

s = (a + b + c) / 2

Table of Contents

Introduction

After reading, test values in the Heron's Formula Calculator to see how s affects area output.

Semi-perimeter is a small symbol with a large role. If s is wrong, every Heron's area result will be wrong even when side lengths are correct.

Main Content

What is it?

Semi-perimeter is not a separate triangle measurement you measure in the field. It is a computed value used inside Heron's formula.

It links perimeter calculations to area through one compact symbol s, which keeps the main area expression shorter and easier to reuse.

Continue with How to Use Heron's Formula for the full workflow, and read Heron's Formula Equation to see where s appears in the final area expression.

Formula

s = (a + b + c) / 2.

If perimeter P = a + b + c, then s = P / 2.

Some students compute P first because it is intuitive: walk around the triangle once, then divide by two.

Units matter. If sides are in meters, s is in meters and area will be in square meters after the full Heron's calculation.

Step-by-step guide

  1. Add sides a, b, and c.
  2. Divide the sum by 2 to get s.
  3. Compute (s - a), (s - b), and (s - c).
  4. Use s in Heron's formula for area.
  5. Keep units consistent with side lengths.

Example

Sides 8, 15, 17: P = 40, s = 20, area = 60 square units.

Sides 3, 4, 5: P = 12, s = 6, area = 6 square units.

Notice that different triangles can share the same s value while having different areas, because side differences change the product inside the square root.

FAQ

Can I skip semi-perimeter and still use Heron's formula?

You still need the s value, even if you compute it mentally as half the perimeter.

Is semi-perimeter the same as perimeter?

No. Semi-perimeter is exactly half of the full perimeter.

Conclusion

Semi-perimeter is the bridge between perimeter and Heron's area result. Master s early and the rest of the formula becomes routine.

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