Triangular Prisms and the "Rectangle Trap"
Grade 7 students in Big Ideas Math Advanced 2 (Chapter 14: Surface Area and Volume) learn that a triangular prism has 2 triangular bases and 3 rectangular lateral faces. A common mistake is assuming all rectangles are identical—they are NOT unless the triangular base is equilateral, since each rectangle width matches a different side of the triangle.
Key Concepts
Property 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.
Examples The Trap: A triangular prism has a triangle base with sides of 3 cm, 4 cm, and 5 cm. The height of the whole prism is 10 cm. You will have 3 DIFFERENT rectangles: Rectangle 1: 3 x 10 = 30 sq cm Rectangle 2: 4 x 10 = 40 sq cm Rectangle 3: 5 x 10 = 50 sq cm (Plus the area of the two triangles!).
Explanation 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!
Common Questions
How many faces does a triangular prism have?
A triangular prism has exactly 5 faces: 2 identical triangular bases and 3 rectangular lateral faces.
Are the rectangular faces of a triangular prism always the same size?
No. Each rectangular face has a width equal to one side of the triangular base. Unless the triangle is equilateral (all sides equal), the three rectangles have different dimensions.
How do you find the surface area of a triangular prism?
Add the areas of the 2 triangular bases plus the areas of the 3 rectangular faces. Each rectangle has width equal to one side of the triangle and length equal to the prism height.
What chapter in Big Ideas Math Advanced 2 covers triangular prism surface area?
Chapter 14: Surface Area and Volume in Big Ideas Math Advanced 2 (Grade 7) covers triangular prisms.
What is the rectangle trap in triangular prism problems?
Many students assume the 3 rectangular faces are identical. They are only identical if the triangular base is equilateral. Always check each side length of the triangle separately.