Lesson 5.75.7 Small Group · Group 1
Start hereWords, worked example, and sentence starters
Learning target With my small group, I can find the surface area of rectangular and triangular prisms — one step at a time, with support.
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 every face |
| Rectangular prismSpanish: Prisma rectangular | A solid box shape with six flat rectangle sides. | 3 congruent pairs |
| Triangular prismSpanish: Prisma triangular | A solid with two triangle ends and three flat rectangle sides. | Shaped like a tent or a wedge of cheese — 2 triangle ends + 3 rectangle sides |
| FaceSpanish: Cara | One flat side of a solid shape. | top, side, end |
| NetSpanish: Plantilla (desarrollo plano) | A flat shape that folds up into a solid. | unfolded box |
| Lateral faceSpanish: Cara lateral | The side faces of a solid, not the top or bottom. | On a triangular prism, the 3 rectangles that wrap around the sides are lateral faces |
How it worksWorked examplesurface area from a net
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A rectangular prism is 9 cm long, 6 cm wide, and 4 cm tall. Find its surface area.
- Unfold it into a net. The 6 faces come in 3 matching pairs.
- Find one face from each pair. 9 × 6 = 54 9 × 4 = 36 6 × 4 = 24
- Add those three. 54 + 36 + 24 = 114
- Each one happens twice, so double. 114 × 2 = 228
Answer: The surface area is 228 square centimeters (228 cm²).
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A rectangular prism is 11 in. long, 8 in. wide, and 2 in. tall. Find its surface area.
- Sketch the net. How many faces, and how many pairs? ,
- One face from each pair: × = · × =
- Third face and sum: × = Total of the three:
- Double it. × 2 = in²
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The prism has faces in matching pairs.
- The three different face areas are , , and .
- I doubled each face area because .
- The surface area is square units.
Word bank surface areanetfacecongruentpairprismunfoldadddoublesquare unitstopside
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 5.75.7 Small Group · Group 1
Group 1Supported practice
Learning target With my small group, I can find the surface area of rectangular and triangular prisms — one step at a time, with support.
-
1Complete each step, then write the final answer.
The net has 2 triangles and 3 rectangles. A triangular prism is 5 in long. Each triangle end has a base of 12 in and a height of 8 in. The two slanted sides are 10 in each. Find the surface area.
- 1What is the area of one triangle end?
- 2What is the area of both triangle ends?
- 3The rectangles are 12 × 5, 10 × 5 and 10 × 5. Add them.
- 4Add the triangles and the rectangles. What is the surface area?
Final answer: -
2Complete each step, then write the final answer.
A ramp is a triangular prism 10 in long. Each triangle end has sides of 5 in, 12 in and 13 in. The 5 in and 12 in sides meet at a square corner. Find the surface area.
- 1Which two sides are the base and height of the triangle?
- 2What is the area of both triangle ends?
- 3Each rectangle is one side × 10. What do the three rectangles add to?
- 4What is the surface area?
Final answer: -
3Complete each step, then write the final answer.
A rectangular prism is 4 cm long, 2 cm wide, and 1 cm tall. Find its surface area.
Show your workHint A rectangular prism has 3 pairs of matching faces. Find each pair, then add.
Final answer: -
4Complete each step, then write the final answer.
A triangular prism is 10 cm long. Its triangle ends have sides of 8 cm, 15 cm and 17 cm. The 8 cm and 15 cm sides meet at a square corner. Find the surface area.
Show your workHint Use the two sides at the square corner for the triangles. Use all three sides for the rectangles.
Final answer: -
5Complete each step, then write the final answer.
A tent with a floor is a triangular prism 5 ft long. Each triangle end has a base of 16 ft and a height of 6 ft. The slanted sides are 10 ft. How much fabric covers the whole tent?
Show your workHint The fabric covers 5 faces: 2 triangles, the floor and 2 slanted sides.
Final answer: -
6Complete 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 workHint Count the faces Rosa added. How many faces does a triangular prism have?
Final answer:
Explain your thinkingHow is the surface area of a triangular prism like the surface area of a box? How is it different?
Sentence starter Both are the same because ___. · A triangular prism has ___ faces, so ___.