Grade 6 Math · Topic 60

Surface Area of Triangular Prisms

A triangular prism has two congruent triangular bases and three rectangular sides connecting them. Its surface area is the sum of those 5 face areas, easily found by sketching the net first.

Lesson alignment: 6.G.A.4 · Take your time. You can return to this lesson whenever you need it.

Explore visually

Unfold a triangular prism

The net has three rectangles and two matching triangular ends.

Think first: How many faces should appear when this solid is unfolded?

Ready? Reveal the model and try your prediction

Swipe horizontally to see the full diagram.

Turn on JavaScript to adjust this model. The examples and practice below work without it.

Follow the worked examples

Read each step, then cover the explanation and see if you can explain why it works.

Worked example 1

A triangular prism has triangle base b = 6, h = 4, and prism length ℓ = 10. The triangle's three sides are 5, 5, 6.

Triangle area: 1/2(6)(4) = 12. Perimeter of base: 5+5+6 = 16. SA = 2(12) + 16(10) = 24 + 160 = 184 sq units.

Answer: 184 sq units

Worked example 2

Triangle base: legs 3 and 4 (right tri), hypotenuse 5. Prism length 8.

Triangle area: 1/2(3)(4) = 6. Perimeter 3+4+5 = 12. SA = 2(6) + 12(8) = 12 + 96 = 108 sq units.

Answer: 108 sq units

Try a few on your own

Work these on paper first. Open “Check” when you are ready to compare your answer.

  1. b=4, h=3; a=3, b=4, c=5; ℓ=6
    Check

    84

  2. b=6, h=4; eq tri sides 6; ℓ=10
    Check

    204

  3. b=8, h=6; sides 6,8,10; ℓ=12
    Check

    336

  4. b=10, h=8; sides 8,10,12; ℓ=5
    Check

    230

  5. b=5, h=4; sides 4,5,6; ℓ=8
    Check

    140

  6. b=12, h=5; sides 5,12,13; ℓ=10
    Check

    360

  7. b=9, h=6; sides 6,9,9; ℓ=7
    Check

    222

  8. b=6, h=5; sides 5,6,7; ℓ=9
    Check

    192

Try this situation 1

A tent has triangular ends with b = 6 ft, h = 4 ft, and slant sides 5 ft each. The tent is 10 ft long. Find total fabric for all 5 faces.

Show a worked solution

Answer: 184 ft².

Tri area 1/2(6)(4) = 12. P = 5+5+6 = 16. SA = 2(12) + 16(10) = 184.

Try this situation 2

A toy ramp is a right-triangular prism with legs 3 and 4 in, hypotenuse 5 in, and length 12 in. Find its surface area.

Show a worked solution

Answer: 156 in².

Tri = 6. P = 12. SA = 2(6) + 12(12) = 12 + 144 = 156.

Fresh questions · saved on this device

Practice this skill

17 question pool

Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.

Choose a session length

Your practice results stay in this browser and appear in the course progress report.

Check what you learned

Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.

1. A triangular prism has an equilateral triangle base with side 4 cm. The height of the triangle is 3.5 cm. The prism length is 6 cm. What is the surface area?

2. Which calculation is correct for finding the surface area of a triangular prism with triangular base area 18 m², perimeter 16 m, and prism length 7 m?

3. A triangular prism has an isosceles triangle base with base 8 m, two equal sides of 5 m, and triangle height 3 m. The length of the prism is 12 m. What is the total surface area?

4. A student finds the surface area of a triangular prism and gets 84 m², forgetting to multiply the triangle area by 2. If the perimeter is 14 m and the prism length is 6 m, what was the triangle area they should have included?

5. A triangular prism has a triangular base with area 20 cm² and perimeter 24 cm. The height of the prism is 7 cm. What is the surface area?

Practice and finish

Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.

Open the practice quiz

Your checkmark, skill-practice sessions, and best exit-check score are saved on this browser and device. The course page can download a progress report to share with a tutor or teacher.

More Grade 6 resources

Use these free materials if you want another explanation, extra paper practice, or a broader review.

Browse free Grade 6 topic lessons ↗Print Grade 6 worksheets ↗Review Grade 6 flashcards ↗Open the formula review ↗Try the Geometry: Area, Surface Area & Volume quiz ↗Try a full practice test ↗