Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
If you cut along the edges of a cereal box and flatten it, you get a net: a flat pattern of rectangles that folds back into the box. Sixth graders draw and recognize nets for three-dimensional figures made of rectangles and triangles, mainly rectangular prisms, triangular prisms and square pyramids, and use them to find surface area.
Surface area is the total area of all the faces, so the net turns a 3D problem into several 2D area problems, using the triangle and rectangle area skills from 6.G.A.1. For a box 5 cm by 3 cm by 2 cm, the net shows two 5 by 3 faces, two 5 by 2 faces and two 3 by 2 faces, giving 30 + 20 + 12 = 62 square centimeters. Students should be able to spot when a pattern is not a valid net (faces would overlap or leave a gap when folded) and apply surface area to real tasks such as wrapping a gift or painting a shed. Surface area is measured in square units, while volume uses cubic units, a distinction many students blur.
From a drawing of a box, students often add only the three faces they can see. A net shows all six faces.
Multiplying length, width and height gives volume, not surface area. Surface area adds face areas and uses square units.
For a pyramid or triangular prism, each triangle's area is 1/2 bh. Students sometimes multiply base by height and double the true answer.
A square pyramid has a base 6 cm on each side. Each triangular face has a base of 6 cm and a height of 5 cm. Find its surface area using a net.
Answer: The surface area is 96 cm².
Unfold real packaging and let students build solids from paper nets. Color-coding matching faces helps students see that a rectangular prism always has three pairs of identical faces.
Assessments often show a net with labeled dimensions and ask for the surface area, or show several patterns and ask which one folds into a given solid.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 52
Pairs of faces: 2 × (4 × 3) = 24, 2 × (4 × 2) = 16 and 2 × (3 × 2) = 12. Total 24 + 16 + 12 = 52 square inches.
Answer: B) 5
A triangular prism has 2 triangular faces and 3 rectangular faces, 5 in total.
Answer: 150
A cube has 6 square faces of 5 × 5 = 25 cm², so 6 × 25 = 150 cm².
Answer: D) Square centimeters
Surface area adds areas of faces, so it is measured in square units.
Answer: 40
Base 4 × 4 = 16. Each triangle 1/2 × 4 × 3 = 6, and four of them make 24. Total 16 + 24 = 40 m².
A full lesson with slides, activities and an exit ticket on nets and surface area, pitched to grade 6 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 6.G.A.4 with an answer key, ready in about a minute.
Make a worksheet →Turn nets and surface area into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Three-dimensional figures whose nets are made of rectangles and triangles, such as rectangular prisms, triangular prisms and pyramids.
No. Circles are not part of this standard. Surface area involving circles comes in grade 7 and beyond.