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Find surface area using nets

A net represents the faces of a three-dimensional solid unfolded into a plane, allowing surface area to be found by calculating the area of each polygonal face and adding the results in square units. This understanding applies to familiar rectangular prisms, triangular prisms, and pyramids, including recognizing congruent faces and avoiding confusion between surface area, which measures exposed faces, and volume, which measures interior space; generalized formulas and more complex solids are not included.

Detailed Explanation: Find surface area using nets

A net shows all the faces of a solid unfolded into one flat shape. To find the surface area, find the area of each face and add the areas together. Use square units because area measures the amount of surface covered.

Example

A net forms a rectangular prism with:

  • length: 55 units
  • width: 33 units
  • height: 22 units

Step 1: Identify the faces

A rectangular prism has three pairs of matching, or congruent, rectangles:

  • 22 rectangles measuring 5×35 \times 3
  • 22 rectangles measuring 5×25 \times 2
  • 22 rectangles measuring 3×23 \times 2

The net shows these six faces unfolded.

Step 2: Find the area of each type of face

Use the area formula for a rectangle:

Area=length×width\text{Area}=\text{length}\times\text{width}

For the 5×35 \times 3 faces:

5×3=155\times3=15

Since there are two:

2×15=302\times15=30

For the 5×25 \times 2 faces:

5×2=105\times2=10

Since there are two:

2×10=202\times10=20

For the 3×23 \times 2 faces:

3×2=63\times2=6

Since there are two:

2×6=122\times6=12

Step 3: Add the areas

30+20+12=6230+20+12=62

The surface area of the rectangular prism is:

62 square units\boxed{62\text{ square units}}

Remember: surface area includes the areas of all the exposed faces in the net. It measures the outside covering of the solid, not the space inside it.

Learn by doing: Find surface area using nets

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    Surface Area of a Rectangular Prism - Count Blocks

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