Determine Surface Area of Prisms
Name Period
Objectives / Objetivos
Content Objective: I can find the surface area of rectangular and triangular prisms.
Language Objective: I can explain my work using the words surface area, rectangular prism, triangular prism, and face.
Key Idea / Idea clave
Surface Area of Prisms. Formula: Surface Area = Sum of areas of all 6 faces. 1. Calculate area of Top & Bottom: 2 × (l · w). 2. Calculate area of Front & Back: 2 × (l · h). 3. Calculate area of Left & Right: 2 × (w · h), then sum all three pairs
I Notice / Observo
- How many faces does a rectangular prism have? A triangular prism?
- What shapes make up the faces of a triangular prism?
I Wonder / Me pregunto
- Which shape uses more paint — a rectangular or triangular prism of similar size?
Vocabulary / Vocabulario
| Term / Término | Definition / Definición |
|---|---|
| Surface Area of Prisms Área de superficie de prismas | The total area of all bases and lateral faces of a prism. Formula: SA = 2B + lateral area. El área total de las bases y caras laterales de un prisma. Fórmula: SA = 2B + área lateral. |
| Surface area Área de superficie | The total area of all the flat sides of a solid. El área total de todos los lados planos de un sólido. |
| Rectangular prism Prisma rectangular | A solid box shape with six flat rectangle sides. Una figura sólida en forma de caja con seis lados rectangulares. |
| Triangular prism Prisma triangular | A solid with two triangle ends and three flat rectangle sides. Un sólido con dos extremos triangulares y tres lados rectangulares. |
| Face Cara | One flat side of a solid shape. Un lado plano de una figura sólida. |
| Net Plantilla (desarrollo plano) | A flat shape that folds up into a solid. Una figura plana que se dobla y forma un sólido. |
Practice Preview / Vista previa de práctica
Read each task. Show your work in the spaces provided and explain how you know.
1. A time capsule is a rectangular prism with l = 5 cm, w = 4 cm, h = 3 cm. What surface area needs paint?
- A 47 cm²
- B 60 cm²
- C 94 cm²
- D 94 cm³
Answer:
2. Calculate the surface area of each rectangular prism time capsule.
Complete each empty cell. Show your reasoning below.
| Capsule | Length | Width | Height | Surface Area |
|---|---|---|---|---|
| Capsule E | 12 in | 8 in | 5 in | |
| Capsule F | 9 cm | 6 cm | 6 cm | |
| Capsule G | 15 ft | 4 ft | 3 ft |
3. A wedge-shaped time capsule is a triangular prism. Its triangular bases have 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 surface area needs paint?
- A 124 in²
- B 160 in²
- C 184 in²
- D 184 in³
Answer:
4. Find the Surface Area Error
Which step has the mistake, and what should it be?
Reflection / Reflexión
One thing I learned today / Una cosa que aprendí hoy: