Determine Surface Area of Prisms

6.GR.4 · Unit 5 · Lesson 7

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 / TérminoDefinition / 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

  1. What is the surface area of a rectangular prism with l = 5 cm, w = 4 cm, h = 3 cm?
    1. 94 cm²
    2. 60 cm²
    3. 94 cm³
    4. 47 cm²
  2. Calculate the surface area of each rectangular prism time capsule.
  3. 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?
    1. 184 in²
    2. 160 in²
    3. 124 in²
    4. 184 in³
  4. Find the Surface Area Error
    1. Step 1: Dimensions — Rectangular prism: l = 12 cm, w = 7 cm, h = 5 cm
    2. Step 2: Formula — SA = 2lw + 2lh + 2wh
    3. Step 3: Calculate — SA = 2(12×7) + 2(12×5) + 2(7×5) = 168 + 120 + 35 = 323 cm²
    4. Step 4: Answer — Surface Area = 323 cm²

    Which step has the mistake? Explain it and write the correct work.

Reflection / Reflexión

One thing I learned today / Una cosa que aprendí hoy: