Surface Area of a Prism Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
A rectangular prism (box) has length 5 cm, width 3 cm, and height 4 cm. Find its surface area.

Solution

  1. 1
    Step 1: For a rectangular prism, the surface area formula is SA=2(lw+lh+wh)SA = 2(lw + lh + wh), which fits the general form SA=2B+PhSA = 2B + Ph for a rectangular base.
  2. 2
    Step 2: Calculate each face pair: lw=5×3=15lw = 5 \times 3 = 15; lh=5×4=20lh = 5 \times 4 = 20; wh=3×4=12wh = 3 \times 4 = 12.
  3. 3
    Step 3: SA=2(15+20+12)=2×47=94SA = 2(15 + 20 + 12) = 2 \times 47 = 94 cm².

Answer

SA =94= 94 cm².
The surface area of a rectangular prism consists of 3 pairs of congruent rectangles. Each pair has area equal to the product of two dimensions. The total is twice the sum of the three face areas. This is the most common prism in everyday life (cereal boxes, shipping boxes, etc.).

About Surface Area of a Prism

The total area of all faces of a prism, found by adding the areas of the two bases and all lateral (side) faces.

Learn more about Surface Area of a Prism →

More Surface Area of a Prism Examples

Example 2 medium

A triangular prism has a triangular base with base 6 cm and height 4 cm, and the prism's length is 1

Example 3 easy

A cube has side length 7 cm. Find its surface area.

Example 4 hard

A prism has a regular hexagonal base with side length 4 cm. The prism has height 10 cm. Find the sur

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