Surface Area of a Prism Math Example 4

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Example 4

hard
A prism has a regular hexagonal base with side length 4 cm. The prism has height 10 cm. Find the surface area. (Area of regular hexagon with side ss: A=332s2A = \frac{3\sqrt{3}}{2}s^2.)

Solution

  1. 1
    Step 1: Find the area of the hexagonal base: B=332(4)2=332×16=243B = \frac{3\sqrt{3}}{2}(4)^2 = \frac{3\sqrt{3}}{2} \times 16 = 24\sqrt{3} cm².
  2. 2
    Step 2: Find the perimeter of the hexagonal base (6 sides of length 4): P=6×4=24P = 6 \times 4 = 24 cm.
  3. 3
    Step 3: Apply the formula: SA=2B+Ph=2(243)+24(10)=483+240SA = 2B + Ph = 2(24\sqrt{3}) + 24(10) = 48\sqrt{3} + 240 cm².
  4. 4
    Step 4: Approximate: 483≈48×1.732=83.148\sqrt{3} \approx 48 \times 1.732 = 83.1, so SA≈83.1+240=323.1SA \approx 83.1 + 240 = 323.1 cm².

Answer

SA=483+240≈323.1SA = 48\sqrt{3} + 240 \approx 323.1 cm².
The general prism formula SA=2B+PhSA = 2B + Ph works for any right prism regardless of the base shape. You only need to know the area and perimeter of the base. For a regular hexagon, the area formula involves 3\sqrt{3} because it is made of 6 equilateral triangles.

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 1 easy

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

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.

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