Surface Area Formulas for Prisms
Surface Area Formulas for Prisms is a skill on Pengi from Section 14.1: Surface Areas of Prisms in Big Ideas Math, Advanced 2.
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 Surface Area Formulas for Prisms?
Surface Area Formulas for Prisms is a skill on Pengi from Section 14.1: Surface Areas of Prisms in Big Ideas Math, Advanced 2.
What grade level is Surface Area Formulas for Prisms for?
Surface Area Formulas for Prisms is part of the Grade 7 Math curriculum, covered in Big Ideas Math, Advanced 2. It is designed for students studying Math at the Grade 7 level.
How can I learn Surface Area Formulas for Prisms?
Pengi offers an AI-guided lesson for Surface Area Formulas for Prisms that walks you through the key concepts step by step. The lesson is aligned to Big Ideas Math, Advanced 2 so the content matches what you see in class.
How do I practice Surface Area Formulas for Prisms?
After learning the concept, use the Practice mode to work through targeted exercises on Surface Area Formulas for Prisms. The AI adapts to your level and gives feedback on each answer so you can identify and fix mistakes.
Which textbook covers Surface Area Formulas for Prisms?
Surface Area Formulas for Prisms is covered in Big Ideas Math, Advanced 2, specifically in Chapter 14: Surface Area and Volume under Section 14.1: Surface Areas of Prisms. Pengi's lesson is aligned directly to this textbook so you can follow along with your class.
Is Surface Area Formulas for Prisms free to study on Pengi?
Yes, the core Learn and Practice modes for Surface Area Formulas for Prisms are available for free on Pengi. No credit card is required to start studying.