Surface Area of Pyramids

6.GR.4 · Unit 10 · Lesson 5

Name   Period

Objectives / Objetivos

Content Objective: I can find the surface area of a pyramid by adding the base area and the lateral faces.

Language Objective: I can explain my work using the words pyramid, slant height, lateral face, and base.

Key Idea / Idea clave

Surface area of a pyramid = base area + the area of all the triangular lateral faces.

I Notice / Observo

  • How many faces does a square pyramid have?
  • What shape is the base? What shape are the side faces?

I Wonder / Me pregunto

  • Why do we use slant height instead of regular height for the triangular faces?

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
Pyramid
Pirámide		A solid with a flat bottom and triangle sides that meet at one point on top.
Un sólido con un fondo plano y lados triangulares que se unen en un punto arriba.
Slant height
Altura inclinada (apotema)		The height of a side triangle, measured along its slanted face.
La altura de un triángulo lateral, medida por su cara inclinada.
Lateral face
Cara lateral		A triangle side of a pyramid, not the bottom.
Un lado triangular de una pirámide, no el fondo.
Base
Base		The flat bottom of a pyramid.
El fondo plano de una pirámide.
Apex
Ápice		The point at the top of a pyramid where the sides meet.
El punto en la parte de arriba de una pirámide donde se unen los lados.
Lateral area
Área lateral		The total area of just the side triangles, not the bottom.
El área total solo de los triángulos laterales, sin el fondo.

Practice Preview / Vista previa de práctica

  1. A square pyramid has a base edge of 5 in and a slant height of 7 in. What is the surface area?
    1. 95 in²
    2. 70 in²
    3. 95 in³
    4. 120 in²
  2. Find the surface area of each square pyramid.
  3. A square pyramid has a base area of 49 cm² and a total lateral area of 84 cm². What is the surface area?
    1. 133 cm²
    2. 84 cm²
    3. 49 cm²
    4. 133 cm³
  4. Find the Surface Area Error
    1. Step 1: Dimensions — Square pyramid: base edge = 10 in, slant height = 8 in
    2. Step 2: Base Area — 10 × 10 = 100 in²
    3. Step 3: Lateral Area — ½ × 10 × 8 = 40 in² (one face). Total lateral = 40 × 3 = 120 in²
    4. Step 4: Answer — SA = 100 + 120 = 220 in²

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

Reflection / Reflexión

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