Surface Area of a Prism Math Example 2

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Example 2

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A triangular prism has a triangular base with base 6 cm and height 4 cm, and the prism's length is 10 cm. The three sides of the triangular base are 5, 5, and 6 cm. Find the total surface area.

Solution

  1. 1
    Step 1: Find the area of the triangular base: B=12×6×4=12B = \frac{1}{2} \times 6 \times 4 = 12 cm².
  2. 2
    Step 2: Find the perimeter of the triangular base: P=5+5+6=16P = 5 + 5 + 6 = 16 cm.
  3. 3
    Step 3: Use the prism surface area formula: SA=2B+Ph=2(12)+16(10)=24+160=184SA = 2B + Ph = 2(12) + 16(10) = 24 + 160 = 184 cm².

Answer

SA =184= 184 cm².
The formula SA=2B+PhSA = 2B + Ph applies to any right prism: 2B2B accounts for the two bases (top and bottom), and PhPh accounts for the lateral surface (the rectangular sides wrapped around the prism). The perimeter PP is the perimeter of the base, and hh is the prism's height (length).

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 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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