Triangular Prism Practice Problems

Formulas you need

• Volume: $V = B \cdot L$
• Surface area: $SA = 2B + (a+b+c)L$

where a, b, c = base triangle sides, L = prism length, B = area of the triangular base

Generate a new problem

Pick a difficulty, work it out, then check your answer. Every press gives a new question — the numbers are drawn fresh each time, so you can keep going.

Warm-up

1. A triangular prism has side a = 5, side b = 5, side c = 5 and prism length L = 5. Find the volume (V).

   Answer & working

   54.13 units³

   V = base area · L = 10.8253 · 5 ≈ 54.13

2. A triangular prism has side a = 4, side b = 2, side c = 4 and prism length L = 2. Find the surface area (SA).

   Answer & working

   27.75 units²

   SA = 2·base + (a+b+c)·L = 7.746 + 20 ≈ 27.75

3. A triangular prism has side a = 4, side b = 5 and side c = 4. Find the base area (A_b).

   Answer & working

   7.81 units²

   base area = √(s(s−a)(s−b)(s−c)) ≈ 7.81

4. A triangular prism has side a = 5, side b = 4, side c = 5 and prism length L = 6. Find the volume (V).

   Answer & working

   54.99 units³

   V = base area · L = 9.1652 · 6 ≈ 54.99

5. A triangular prism has side a = 3, side b = 2, side c = 2 and prism length L = 1. Find the surface area (SA).

   Answer & working

   10.97 units²

   SA = 2·base + (a+b+c)·L = 3.9686 + 7 ≈ 10.97

Core practice

1. A triangular prism has side a = 6, side b = 5, side c = 6 and prism length L = 1. Find the volume (V).

   Answer & working

   13.64 units³

   V = base area · L = 13.6359 · 1 ≈ 13.64

2. A triangular prism has side a = 7, side b = 2, side c = 8 and prism length L = 10. Find the surface area (SA).

   Answer & working

   182.87 units²

   SA = 2·base + (a+b+c)·L = 12.8744 + 170 ≈ 182.87

3. A triangular prism has side a = 2, side b = 9 and side c = 10. Find the base area (A_b).

   Answer & working

   8.18 units²

   base area = √(s(s−a)(s−b)(s−c)) ≈ 8.18

4. A triangular prism has side a = 6, side b = 2, side c = 7 and prism length L = 7. Find the volume (V).

   Answer & working

   38.94 units³

   V = base area · L = 5.5621 · 7 ≈ 38.94

5. A triangular prism has side a = 7, side b = 5, side c = 4 and prism length L = 11. Find the surface area (SA).

   Answer & working

   195.6 units²

   SA = 2·base + (a+b+c)·L = 19.5959 + 176 ≈ 195.6

Stretch

1. A triangular prism has side a = 1.5, side b = 8.5, side c = 8.5 and prism length L = 6.5. Find the volume (V).

   Answer & working

   41.28 units³

   V = base area · L = 6.3501 · 6.5 ≈ 41.28

2. A triangular prism has side a = 8.5, side b = 1.5, side c = 9.5 and prism length L = 9.5. Find the surface area (SA).

   Answer & working

   195.28 units²

   SA = 2·base + (a+b+c)·L = 10.0273 + 185.25 ≈ 195.28

3. A triangular prism has side a = 3.5, side b = 3.5 and side c = 5.5. Find the base area (A_b).

   Answer & working

   5.95 units²

   base area = √(s(s−a)(s−b)(s−c)) ≈ 5.95

4. A triangular prism has side a = 10, side b = 1.5, side c = 10 and prism length L = 8.5. Find the volume (V).

   Answer & working

   63.57 units³

   V = base area · L = 7.4789 · 8.5 ≈ 63.57

5. A triangular prism has side a = 7.5, side b = 4.5, side c = 7.5 and prism length L = 2.5. Find the surface area (SA).

   Answer & working

   80.95 units²

   SA = 2·base + (a+b+c)·L = 32.1954 + 48.75 ≈ 80.95