Surface Area Formulas for Prisms
Surface Area Formulas for Prisms is a Grade 7 math skill in Big Ideas Math Advanced 2, Chapter 14: Surface Area and Volume. Students learn formulas for cubes (SA = 6L squared), rectangular prisms (SA = 2(LW + LH + WH)), and triangular prisms (SA = 2 times base area + perimeter of base times height). These formulas calculate the total area of all outer faces of 3D prisms.
Key Concepts
Property Cube whose edge is of length $L$: Surface Area $= 6L^2$ Rectangular Prism of length $L$, height $H$ and width $W$: Surface Area $= 2(LW + LH + WH)$ Triangular Prism of height $H$ based on a triangle with side lengths $A$, $B$, $C$ and base area $B {area}$: Surface Area $= 2B {area} + (A + B + C)H$.
Examples A cube with an edge length of 4 cm has a Surface Area of $6(4^2) = 6 \times 16 = 96$ square cm. A rectangular prism is 5 in long, 3 in wide, and 6 in high. Its Surface Area is $2(5 \times 3 + 5 \times 6 + 3 \times 6) = 2(15 + 30 + 18) = 126$ square in. A triangular prism is 8 cm high and its base is a right triangle with legs 3 cm and 4 cm, and hypotenuse 5 cm. The base area is $\frac{1}{2}(3 \times 4) = 6$ square cm. Its Surface Area is $2(6) + (3+4+5)(8) = 12 + 96 = 108$ square cm.
Explanation Surface area measures the total area of all the outside faces of a 3D shape. Think of it as how much wrapping paper you would need to completely cover the object. For prisms, we calculate the area of all faces and add them together using these formulas.
Common Questions
What is the surface area formula for a rectangular prism?
SA = 2(LW + LH + WH), where L is length, W is width, and H is height. For example, a prism that is 5 by 3 by 6 inches has SA = 2(15 + 30 + 18) = 126 square inches.
How do you find the surface area of a cube?
SA = 6L squared, where L is the edge length. For example, a cube with edge length 4 cm has SA = 6 x 16 = 96 square centimeters.
What is the surface area formula for a triangular prism?
SA = 2 times the base area plus the perimeter of the triangular base times the height: SA = 2B + (A + B + C)H. First find the area of the triangular face, then add the area of all three rectangular faces.
What does surface area measure?
Surface area measures the total area of all the outer faces of a 3D shape. Think of it as how much wrapping paper you would need to cover the entire object.