Lesson 6: Find Surface Areas of Prisms

Property

For a rectangular prism with length $L$, width $W$, and height $H$:

Surface Area: $S = 2LH + 2LW + 2WH$

Property

A cube is a rectangular solid whose length, width, and height are equal. For any cube with sides of length $s$:

Surface Area: $S = 6s^2$

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!