Lesson 5.7Surface Area of Triangular Prisms
Start hereWords, worked example, and sentence starters
Learning target I can find the surface area of rectangular and triangular prisms.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| Surface areaSpanish: Área de superficie | The total area of all the flat sides of a solid. | add all 5 faces |
| Rectangular prismSpanish: Prisma rectangular | A solid box shape with six flat rectangle sides. | A box with 6 flat rectangle sides: top, bottom, front, back, left, right |
| Triangular prismSpanish: Prisma triangular | A solid with two triangle ends and three flat rectangle sides. | a tent shape |
| FaceSpanish: Cara | One flat side of a solid shape. | A triangular prism has 5 faces: 2 triangles + 3 rectangles |
| NetSpanish: Plantilla (desarrollo plano) | A flat shape that folds up into a solid. | Unfold a triangular prism flat: you see 2 triangles and 3 rectangles side by side |
| Lateral faceSpanish: Cara lateral | The side faces of a solid, not the top or bottom. | the 3 rectangles |
How it worksWorked examplesurface area of a triangular prism
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A triangular prism is 11 cm long. Each triangular end is a right triangle with legs of 6 cm and 8 cm and a longest side of 10 cm. Find the surface area.
- The net has 2 congruent triangles and 3 rectangles.
- Both triangular ends: 2 × (½ × 6 × 8) = 48
- Every rectangle uses the length 11. 6 × 11 = 66 8 × 11 = 88 10 × 11 = 110
- Add every face. 48 + 66 + 88 + 110 = 312
Answer: The surface area is 312 square centimeters (312 cm²).
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A triangular prism is 7 in. long. Each triangular end is a right triangle with legs of 9 in. and 12 in. and a longest side of 15 in. Find the surface area.
- Sketch the net. Triangles: Rectangles:
- Both triangular ends: 2 × (½ × × ) =
- Each rectangle uses the length: , ,
- Add every face. + + + = in²
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The net has triangles and rectangles.
- Each triangular end has an area of square units.
- Every rectangle uses as one of its sides.
- The surface area is because I added .
Word bank triangular prismnetfacelateral facebasetrianglerectanglecongruentaddsurface areasquare unitslength
Watch outA common mistake
A common mistake in Surface Area of Prisms is confusing surface area with volume — multiplying l × w × h (which finds the space INSIDE the prism, in cubic units) instead of adding the areas of all the faces (SA = 2lw + 2lh + 2wh, in square units). A second common slip is forgetting to double one face pair, like writing 2(l×w) + 2(l×h) + (w×h) instead of + 2(w×h) — always count all 6 faces (or all 5 for a triangular prism) before you submit.
Lesson 5.7Surface Area of Triangular Prisms
Apply Day · Version ASupported practice
Learning target I can find the surface area of rectangular and triangular prisms.
-
1Complete each step, then write the final answer.
A rectangular prism is 6 in long, 2 in wide, and 1 in tall. Find its surface area.
Show your workHint Find each pair of matching faces. Then add.
Final answer: -
2Complete each step, then write the final answer.
A triangular prism is 2 cm long. Each triangle end has a base of 12 cm and a height of 8 cm. The slanted sides are 10 cm. Find the surface area.
Show your workHint Find the 2 triangles. Then find the 3 rectangles. Add all 5 faces.
Final answer: -
3Complete each step, then write the final answer.
A triangular prism is 3 in long. Its triangle ends have sides of 6 in, 8 in and 10 in. The 6 in and 8 in sides meet at a square corner. Find the surface area.
Show your workHint The sides at the square corner are the base and height of the triangle.
Final answer:
Lesson 5.7Surface Area of Triangular Prisms
Apply Day · Version BCore practice
Learning target I can find the surface area of rectangular and triangular prisms.
-
1Complete each step, then write the final answer.
Rosa finds the surface area of a triangular prism. The rectangles are 12, 16 and 20 square inches. Each triangle end is 24 square inches. She adds 12 + 16 + 20 + 24 = 72. What is the correct surface area?
Show your workFinal answer: -
2Complete each step, then write the final answer.
A triangular prism is 2.5 cm long. Each triangle end has a base of 16 cm and a height of 15 cm. The slanted sides are 17 cm. Find the surface area.
Show your workFinal answer: -
3Complete each step, then write the final answer.
A triangular prism is 3 cm long. Each triangle end has a base of 24 cm and a height of 5 cm. The slanted sides are 13 cm. Find the surface area.
Show your workFinal answer:
Lesson 5.7Surface Area of Triangular Prisms
Apply Day · ChallengeExtension
Learning target I can find the surface area of rectangular and triangular prisms.
-
1Circle the letter of the best answer. Show how you know.
A rectangular prism measures 6 cm long, 4 cm wide, and 2 cm tall. What is its surface area?
- A24 square centimeters
- B44 square centimeters
- C48 square centimeters
- D88 square centimeters
FormulaPut the numbers inWork it outAnswer with its unit -
2Complete each step, then write the final answer.
A prism is 2 cm long. Its right-triangle ends have sides of 9 cm, 12 cm and 15 cm, with the square corner between 9 cm and 12 cm. Mo uses 1/2 × 12 × 15 for each end. Find the correct surface area.
Show your workFinal answer: -
3Complete each step, then write the final answer.
A triangular prism is 6 in long. Its triangle ends have sides of 7 in, 24 in and 25 in. The 7 in and 24 in sides meet at a square corner. Find the surface area.
Show your workFinal answer: