Surface Area - Pyramids

Examples, videos, and solutions to help Grade 7 students learn how to find the surface area of three-dimensional objects whose surface area is composed of triangles and quadrilaterals, specifically focusing on pyramids.

New York State Common Core Math Grade 7, Module 3, Lesson 22

Worksheets for Grade 7

Lesson 22 Student Outcomes

• Students find the surface area of three-dimensional objects whose surface area is composed of triangles and quadrilaterals, specifically focusing on pyramids. They use polyhedron nets to understand that surface area is simply the sum of the area of the lateral faces and the area of the base(s).

Lesson 22 Classwork

Opening Exercise
What is the area of the composite figure in the diagram? Is the diagram a net for a three-dimensional image? If so, sketch the image. If not, explain why.

Example 1
The pyramid in the picture has a square base, and its lateral faces are triangles that are exact copies of one another. Find the surface area of the pyramid.

Example 2: Using Cubes
There are 13 cubes glued together forming the solid in the diagram. The edges of each cube are 1/4 inch in length. Find the surface area of the solid.

Example 3
Find the total surface area of the wooden jewelry box. The sides and bottom of the box are all 1/4 inch thick. What are the faces that make up this box?
How does this box compare to other objects that you have found the surface area of?

Closing
Some strategies for finding the surface area of solids are creating nets, adding the areas of polygonal faces, counting square faces, and adding their areas.

Show Step-by-step Solutions

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.