In this Grade 6 lesson from Pengi Math Chapter 6: Geometry, students learn to interpret nets as unfolded three-dimensional figures and identify all faces of prisms and pyramids. They practice calculating surface area by using nets, and develop the ability to distinguish surface area from volume.
Section 1
Finding Surface Area Using Nets
A net is a 2D pattern that can be folded to form a 3D solid. To find surface area using nets:
(1) identify all faces in the net;
(2) calculate the area of each face;
(3) sum all areas: Surface Area =
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
Finding Surface Area Using Nets
A net is a 2D pattern that can be folded to form a 3D solid. To find surface area using nets:
(1) identify all faces in the net;
(2) calculate the area of each face;
(3) sum all areas: Surface Area =
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!