Geometry

Lesson 18

Objective

 Find the surface area of right pyramids.

Common Core Standards

Core Standards

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  • 7.G.B.6 — Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Foundational Standards

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  • 6.G.A.4

Criteria for Success

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  1. Use a net of a three-dimensional figure to determine the surface area.
  2. Find efficient ways to determine surface area of right pyramids.
  3. Write numerical expressions to represent surface area. 

Tips for Teachers

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Lessons 17 and 18 engage students in finding the surface area of prisms and pyramids. Students leverage their skills with numerical expressions to organize and represent their work in finding the surface area. Lesson 17 focused on prisms and Lesson 18 focuses on pyramids. In Lesson 21, students will revisit surface area as it compares to volume in real-world contexts.

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

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Anchor Problems

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Problem 1

Draw a net of the square pyramid. Then calculate the surface area.

Guiding Questions

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References

EngageNY Mathematics Grade 7 Mathematics > Module 6 > Topic D > Lesson 23Opening Exercise

Grade 7 Mathematics > Module 6 > Topic D > Lesson 23 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Problem 2

The right hexagonal pyramid has a hexagon base with equal-length sides. The lateral faces of the pyramid are all triangles (that are exact copies of one another) with heights of 15 feet. Find the surface area of the pyramid.

Guiding Questions

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References

EngageNY Mathematics Grade 7 Mathematics > Module 3 > Topic C > Lesson 22Exit Ticket #1

Grade 7 Mathematics > Module 3 > Topic C > Lesson 22 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

Target Task

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Cinema Theaters created a new popcorn box in the shape of a square pyramid. The new popcorn box has the dimensions shown below and does not include a lid. How much cardboard, in square inches, does the new popcorn box use?

Mastery Response

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