In this Grade 6 lesson from Big Ideas Math, Course 1 (Chapter 8), students learn how to find the surface area of rectangular and triangular prisms by using nets to identify and calculate the area of each face, then summing those areas. The lesson introduces key vocabulary including surface area and net, and applies the standard formula for triangle area to work with triangular prism faces. Students practice drawing two-dimensional nets, labeling bases and lateral faces, and solving real-life measurement problems aligned with Common Core standard 6.G.4.
Section 1
Introduction to Nets: Drawing a Net for a Prism
A net is a two-dimensional pattern that can be folded to form a three-dimensional solid. To draw a net:
1) identify all faces of the prism,
2) arrange faces so they share edges appropriately,
3) ensure the pattern can fold into the original shape.
Section 2
Surface Area of a Rectangular Prism
A rectangular prism has 6 rectangular faces. Because opposite faces are exactly the same, you have 3 identical pairs.
The formula for Surface Area (SA) using length (l), width (w), and height (h) is:
You don't have to calculate 6 completely different rectangles! Just find the area of the Bottom, the Front, and one Side. Since every face has an exact twin opposite to it, just multiply each of those three areas by 2, and add them all up.
Section 3
Triangular Prisms and the "Rectangle Trap"
A triangular prism has exactly 5 faces: 2 identical triangular bases and 3 rectangular sides.
To find the total surface area, find the area of the 2 triangles and the 3 rectangles, then add them together.
Beware of the biggest trap in 7th-grade geometry! Many students assume the 3 rectangular sides of a triangular prism are always identical. They are NOT! The width of each rectangle connects to a side of the triangle. Unless the triangle is perfectly equilateral (all 3 sides equal), those three rectangular faces will be completely different sizes. Always unfold it into a net in your mind first!
Expand to review the lesson summary and core properties.
Section 1
Introduction to Nets: Drawing a Net for a Prism
A net is a two-dimensional pattern that can be folded to form a three-dimensional solid. To draw a net:
1) identify all faces of the prism,
2) arrange faces so they share edges appropriately,
3) ensure the pattern can fold into the original shape.
Section 2
Surface Area of a Rectangular Prism
A rectangular prism has 6 rectangular faces. Because opposite faces are exactly the same, you have 3 identical pairs.
The formula for Surface Area (SA) using length (l), width (w), and height (h) is:
You don't have to calculate 6 completely different rectangles! Just find the area of the Bottom, the Front, and one Side. Since every face has an exact twin opposite to it, just multiply each of those three areas by 2, and add them all up.
Section 3
Triangular Prisms and the "Rectangle Trap"
A triangular prism has exactly 5 faces: 2 identical triangular bases and 3 rectangular sides.
To find the total surface area, find the area of the 2 triangles and the 3 rectangles, then add them together.
Beware of the biggest trap in 7th-grade geometry! Many students assume the 3 rectangular sides of a triangular prism are always identical. They are NOT! The width of each rectangle connects to a side of the triangle. Unless the triangle is perfectly equilateral (all 3 sides equal), those three rectangular faces will be completely different sizes. Always unfold it into a net in your mind first!