GeometryFormula

Triangle Practice Problems

15 triangle problems with full worked solutions, graded from warm-up to stretch — plus an unlimited supply you can generate yourself. Every answer is computed by the same verified function that powers the triangle explorer, so the solutions cannot disagree with the formulas. Free, no account, nothing to install.

Formulas you need

  • Area (base & height): A=12bhA = \tfrac{1}{2} b h
  • Area (Heron’s): A=s(s−a)(s−b)(s−c)A = \sqrt{s(s-a)(s-b)(s-c)}
  • Semiperimeter: s=a+b+c2s = \dfrac{a+b+c}{2}
  • Perimeter: P=a+b+cP = a + b + c

where a, b, c = the three side lengths, b = base, h = height (perpendicular to base), s = semiperimeter (a+b+c)/2, A = area

Generate a new problem

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Warm-up

  1. A triangle has side a = 5, side b = 5 and side c = 6. Find the area (A).

    Answer & working

    12 units²

    A = √(s(s−a)(s−b)(s−c)) = √(8·3·3·2) = 12

  2. A triangle has side a = 3, side b = 3 and side c = 1. Find the perimeter (P).

    Answer & working

    7 units

    P = a + b + c = 3 + 3 + 1 = 7

  3. A triangle has side a = 6, side b = 3 and side c = 5. Find the semiperimeter (s).

    Answer & working

    7 units

    s = P / 2 = 14 / 2 = 7

  4. A triangle has side a = 4, side b = 3 and side c = 6. Find the area (A).

    Answer & working

    5.33 units²

    A = √(s(s−a)(s−b)(s−c)) = √(6.5·2.5·3.5·0.5) ≈ 5.33

  5. A triangle has side a = 2, side b = 2 and side c = 2. Find the perimeter (P).

    Answer & working

    6 units

    P = a + b + c = 2 + 2 + 2 = 6

Core practice

  1. A triangle has side a = 10, side b = 7 and side c = 5. Find the area (A).

    Answer & working

    16.25 units²

    A = √(s(s−a)(s−b)(s−c)) = √(11·1·4·6) ≈ 16.25

  2. A triangle has side a = 4, side b = 5 and side c = 3. Find the perimeter (P).

    Answer & working

    12 units

    P = a + b + c = 4 + 5 + 3 = 12

  3. A triangle has side a = 8, side b = 11 and side c = 10. Find the semiperimeter (s).

    Answer & working

    14.5 units

    s = P / 2 = 29 / 2 = 14.5

  4. A triangle has side a = 10, side b = 11 and side c = 10. Find the area (A).

    Answer & working

    45.93 units²

    A = √(s(s−a)(s−b)(s−c)) = √(15.5·5.5·4.5·5.5) ≈ 45.93

  5. A triangle has side a = 10, side b = 4 and side c = 10. Find the perimeter (P).

    Answer & working

    24 units

    P = a + b + c = 10 + 4 + 10 = 24

Stretch

  1. A triangle has side a = 8.5, side b = 9.5 and side c = 7.5. Find the area (A).

    Answer & working

    30.41 units²

    A = √(s(s−a)(s−b)(s−c)) = √(12.75·4.25·3.25·5.25) ≈ 30.41

  2. A triangle has side a = 7.5, side b = 7.5 and side c = 5.5. Find the perimeter (P).

    Answer & working

    20.5 units

    P = a + b + c = 7.5 + 7.5 + 5.5 = 20.5

  3. A triangle has side a = 10.5, side b = 11.5 and side c = 11.5. Find the semiperimeter (s).

    Answer & working

    16.75 units

    s = P / 2 = 33.5 / 2 = 16.75

  4. A triangle has side a = 1.5, side b = 5.5 and side c = 5.5. Find the area (A).

    Answer & working

    4.09 units²

    A = √(s(s−a)(s−b)(s−c)) = √(6.25·4.75·0.75·0.75) ≈ 4.09

  5. A triangle has side a = 9.5, side b = 4.5 and side c = 12. Find the perimeter (P).

    Answer & working

    26 units

    P = a + b + c = 9.5 + 4.5 + 12 = 26

Answers are recomputed from the verified triangle function every time this page is built, and every printed line is checked to evaluate correctly. Content last reviewed August 2026. Found a mistake? Tell us — we correct and republish.

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