10B Surface Area & Nets Study Guide

Key Vocabulary

Surface Area — the total area of ALL the outside faces of a 3D shape. (área de superficie)

Net — a flat pattern that can be folded to make a 3D shape. It shows every face. (desarrollo / red)

Face — a flat surface of a 3D shape. (cara)

Edge — the line segment where two faces meet. (arista)

Vertex — a corner point where edges meet (plural: vertices). (vértice)

Visual — Net of a Rectangular Prism

A rectangular prism has 6 faces that come in 3 pairs:

         +------+
         | TOP  |
         | l×w  |
  +------+------+------+------+
  | LEFT | FRONT| RIGHT| BACK |
  | w×h  | l×h  | w×h  | l×h  |
  +------+------+------+------+
         |BOTTOM|
         | l×w  |
         +------+

  3 pairs of identical faces:
    2 faces of l × w  (top & bottom)
    2 faces of l × h  (front & back)
    2 faces of w × h  (left & right)

Step-by-Step: Finding Surface Area

1 Identify all faces of the 3D shape. A rectangular prism has 6 faces.
2 Find the area of each face (length × width for each rectangle).
3 Add all the areas together.

Example: l = 5, w = 3, h = 2
Top & Bottom: 2 × (5 × 3) = 2 × 15 = 30
Front & Back: 2 × (5 × 2) = 2 × 10 = 20
Left & Right: 2 × (3 × 2) = 2 × 6 = 12
SA = 30 + 20 + 12 = 62 square units

Formula Box

SA = 2lw + 2lh + 2wh

l = length, w = width, h = height

Watch Out!

Don't forget — a rectangular prism has 6 faces, not 4! There are 3 PAIRS of matching faces.
Surface area is in SQUARE units (cm², in²), NOT cubic units. Volume is cubic; surface area is square.
A net shows all faces flat. When you fold it up, it makes the 3D shape. Use the net to make sure you count every face.
A cube has 6 identical square faces. SA of a cube = 6s².

Practice Problems

1. Find the surface area: l = 4 cm, w = 3 cm, h = 2 cm.
SA = 2(4×3) + 2(4×2) + 2(3×2) = ?

2. A cube has sides of 5 in. What is the surface area? (SA = 6 × s²)

3. How many faces does a rectangular prism have?