Unit 10 · Standard 6.G.4
Surface Area of Prisms
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
Paint every outside surface of a box — the total painted area is the surface area
Surface area
The total area of all the flat sides of a solid.
A box with 6 flat rectangle sides: top, bottom, front, back, left, right
Rectangular prism
A solid box shape with six flat rectangle sides.
Shaped like a tent or a wedge of cheese — 2 triangle ends + 3 rectangle sides
Triangular prism
A solid with two triangle ends and three flat rectangle sides.
A triangular prism has 5 faces: 2 triangles + 3 rectangles
Face
One flat side of a solid shape.
Unfold a triangular prism flat: you see 2 triangles and 3 rectangles side by side
Net
A flat shape that folds up into a solid.
On a triangular prism, the 3 rectangles that wrap around the sides are lateral faces
Lateral face
The side faces of a solid, not the top or bottom.
Key Ideas & Notes
- Your class is painting the outside of different time capsule shapes to protect them from weather.
- Some capsules are rectangular prisms and others are triangular prisms (wedge-shaped).
- To buy the right amount of paint, you need to calculate the surface area of each shape!
- Calculate the surface area of each time capsule shape. For rectangular prisms, use SA = 2lw + 2lh + 2wh. For triangular prisms, find the area of each face and add them up.
Think About It
- How many faces does a rectangular prism have? A triangular prism?
- What shapes make up the faces of a triangular prism?
- How is finding surface area different from finding volume?
My Notes
Guided Examples
Example 1
What is the surface area of a rectangular prism with l = 5 cm, w = 4 cm, h = 3 cm?
Solution: SA = 2(5×4) + 2(5×3) + 2(4×3) = 40 + 30 + 24 = 94 cm².
Answer: A. 94 cm²
Example 2
How many faces does a triangular prism have?
Solution: A triangular prism has 5 faces: 2 triangular bases and 3 rectangular lateral faces.
Answer: A. 5
Example 3
A triangular prism has two triangular bases each with area 12 cm² and three rectangular faces with areas 30 cm², 40 cm², and 40 cm². What is the total surface area?
Solution: SA = 2(12) + 30 + 40 + 40 = 24 + 110 = 134 cm².
Answer: A. 134 cm²
Write About the Math The Writing Revolution
I can explain my work using the words surface area, rectangular prism, triangular prism, and face.
1. Kernel Sentence subject + verb
Model: Surface area is the total area of all the flat sides of a solid.Área de superficie es el área total de todos los lados planos de un sólido.
Write a kernel sentence about surface area. Use a subject and a verb.Escribe una oración base sobre área de superficie. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Surface area matters in mathÁrea de superficie importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Surface area matters in math because ___.Área de superficie importa en matemáticas porque ___.
Surface area matters in math, but ___.Área de superficie importa en matemáticas, pero ___.
Surface area matters in math, so ___.Área de superficie importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about surface area.Di un hecho verdadero sobre surface area.
Surface area ___.
Ask a question about surface area.Haz una pregunta sobre surface area.
How does ___ ?¿Cómo ___ ?
Show excitement about surface area.Muestra entusiasmo sobre surface area.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with surface area.Dile a un compañero qué hacer con surface area.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
Each face has area ___.Cada cara tiene área ___.
The total surface area is ___.El área total de la superficie es ___.
I would use this to ___.Usaría esto para ___.
Try It
Solve on your own. Check the answer key when you are done.
1. A triangular prism has two triangular bases each with area 12 cm² and three rectangular faces with areas 30 cm², 40 cm², and 40 cm². What is the total surface area?
- 134 cm²
- 110 cm²
- 122 cm²
- 134 cm³
2. A triangular prism has triangular bases with base 6 in and height 4 in. The prism is 10 in long and the two slant sides of the triangle are each 5 in. What is the surface area?
- 184 in²
- 160 in²
- 124 in²
- 184 in³
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
A company ships products in two container options: a rectangular prism (8 × 6 × 4 in) or a triangular prism (triangle base 8 in, triangle height 6 in, prism length 8 in, slant sides 6.3 in each). Both must be wrapped in protective film. Which shape uses LESS film? Show your work.
Sentence starter: Rectangular prism SA = 2(___) + 2(___) + 2(___) = ___ in². Triangular prism SA = 2(___) + ___ + ___ + ___ = ___ in². The ___ uses less film because ___.
Reflect — Exit Ticket
A rectangular prism has l = 8 ft, w = 6 ft, h = 3 ft. What is the surface area?
- 180 ft²
- 144 ft²
- 180 ft³
- 90 ft²
Answer Key & Teacher Guide
- Try It 1: A. 134 cm² — SA = 2(12) + 30 + 40 + 40 = 24 + 110 = 134 cm².
- Try It 2: A. 184 in² — Triangular bases: 2 × (½ × 6 × 4) = 24 in². Three rectangular faces: 6(10) + 5(10) + 5(10) = 60 + 50 + 50 = 160 in². SA = 24 + 160 = 184 in².
- Exit Ticket: A. 180 ft² — SA = 2(8×6) + 2(8×3) + 2(6×3) = 96 + 48 + 36 = 180 ft². Surface area uses square units (ft²).
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Surface area is the total area of all the flat sides of a solid.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).