Determine Surface Area of Pyramids

6.GR.4 · Unit 5 · Lesson 8

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 Pyramids. Formula: Surface Area = Base Area + Sum of Triangular Lateral Faces. 1. Calculate area of base polygon (square, rectangle, or triangle). 2. Calculate area of each triangular face using ½ × base × slant height. 3. Add the base area and all triangular face areas together

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
Surface Area of Pyramids
Área de superficie de pirámides		The total area of a pyramid's base and triangular faces. Formula: SA = B + lateral area.
El área total de la base y las caras triangulares de una pirámide. Fórmula: SA = B + área lateral.
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.

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: