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Perimeter of a Triangle Examples

Worked examples show how to add sides and when to use simplified rules for special triangles.

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Triangle sketch and measuring tools on archival paper

Quick Answer

Add three sides, or use P = 2a + b or P = 3a when the triangle type allows.

Formula

  • Scalene: P = a + b + c
  • Right triangle: add leg + leg + hypotenuse

Introduction

Check each example on the home calculator under 3 sides when all edges are known.

Examples turn abstract formulas into numbers you can picture. They also show when a shortcut is faster than writing three separate addends.

Review the symbol rules in the perimeter of a triangle formula article if you need a refresher before you work through the cases below.

Main Content

Example types

Scalene, isosceles, equilateral, and right triangles each appear often in textbooks and in practical sketches.

A scalene example forces full addition. An equilateral example rewards multiplication. An isosceles example sits between those extremes.

Right triangles still use perimeter = sum of three sides. The Pythagorean theorem helps when a leg is missing, but the final step is always addition around the outline.

Rules used

  • P = a + b + c
  • P = 2a + b
  • P = 3a

Pick the rule that matches equal sides on your diagram before you substitute numbers.

When no sides match, stay with P = a + b + c and validate the triple with triangle inequality.

Unequal-side practice is covered in more detail in the scalene triangle perimeter calculator guide, which walks through validity checks before you add.

Worked examples

Study each case, then cover the answer and solve again from scratch.

  1. Scalene Sides 5, 6, and 7 → P = 5 + 6 + 7 = 18. No shortcut applies.
  2. Isosceles Sides 9, 9, and 4 → P = 9 + 9 + 4 = 22, or P = 2(9) + 4 = 22.
  3. Equilateral Side 7 → P = 3(7) = 21.
  4. Right triangle Legs 3 and 4, hypotenuse 5 → P = 3 + 4 + 5 = 12.
  5. Real-world trim Triangular sign with sides 2 ft, 2 ft, and 2.5 ft → P = 6.5 ft of edging.
  6. Survey sketch Plot sides 14 m, 18 m, and 22 m → P = 54 m along the boundary.

Practice tip

Cover the answer, solve on paper, then confirm with the calculator.

Rotate through one scalene, one isosceles, and one equilateral problem per study session so you recognize symmetry cues on future tests.

If a word problem hides the numbers in sentences, switch to triangle perimeter word problems for reading strategies before you return to numeric drills here.

FAQ

Do right triangles need a special perimeter formula?
No. Add the three side lengths. The Pythagorean theorem helps find a missing side when needed.
Can perimeter be a decimal?
Yes. Construction and calculator work often produce decimal perimeter totals in the same unit as the sides.

Conclusion

Practice each triangle type until addition and shortcuts feel automatic.

Explore equilateral and isosceles guides when you want type-specific depth beyond these samples.

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