Determine Surface Area of Pyramids
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 / Término | Definition / 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
Read each task. Show your work in the spaces provided and explain how you know.
1. A square pyramid has a base edge of 5 in and a slant height of 7 in. What is the surface area?
- A 70 in²
- B 95 in²
- C 95 in³
- D 120 in²
Answer:
2. Find the surface area of each square pyramid.
Complete each empty cell. Show your reasoning below.
| Pyramid | Base Edge | Slant Height | Base Area | Total SA |
|---|---|---|---|---|
| Pyramid X | 12 in | 10 in | ||
| Pyramid Y | 8 cm | 6 cm | ||
| Pyramid Z | 14 ft | 11 ft |
3. A square pyramid has a base area of 49 cm² and a total lateral area of 84 cm². What is the surface area?
- A 49 cm²
- B 84 cm²
- C 133 cm²
- D 133 cm³
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: