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Calculate the surface area of prisms

Surface area of a prism is the total area of all its two congruent, parallel bases and its lateral faces, measured in square units. Learners determine it by interpreting a net or applying SA=2B+PhSA=2B+Ph, where BB is the area of a base, PP its perimeter, and hh the prism length, including rectangular and other familiar right prisms; this distinguishes surface area from volume and supports later geometric and algebraic reasoning.

Detailed Explanation: Calculate the surface area of prisms

Surface area is the total area covering every outside face of a prism. It includes:

  • two congruent bases
  • all the lateral faces connecting the bases

For a prism, use

SA=2B+PhSA=2B+Ph

where:

  • BB is the area of one base
  • PP is the perimeter of one base
  • hh is the length of the prism

The answer is written in square units because we are finding area, not volume.

Example: Find the surface area of a rectangular prism with a base that is 33 units by 44 units and a prism length of 1010 units.

Step 1: Find the area of one base.

The base is a rectangle:

B=3⋅4=12 square unitsB=3\cdot4=12\text{ square units}

Step 2: Find the perimeter of the base.

P=3+4+3+4=14 unitsP=3+4+3+4=14\text{ units}

Step 3: Substitute into the formula.

SA=2B+PhSA=2B+Ph SA=2(12)+14(10)SA=2(12)+14(10)

Step 4: Calculate.

SA=24+140=164SA=24+140=164

The surface area of the prism is

164 square units\boxed{164\text{ square units}}

The 2424 represents the two bases, and the 140140 represents the total area of the four lateral faces.

Learn by doing: Calculate the surface area of prisms

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Surface Area of a Rectangular Prism - Calculate


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