Nets Math Example 1

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

Example 1

easy
Draw and describe the net of a rectangular prism (box) with dimensions 55 cm ×3\times 3 cm ×2\times 2 cm, and use the net to find the total surface area.

Solution

  1. 1
    Step 1: A rectangular prism has 6 faces arranged in 3 pairs of congruent rectangles: two 5×35 \times 3 faces (top/bottom), two 5×25 \times 2 faces (front/back), and two 3×23 \times 2 faces (left/right).
  2. 2
    Step 2: The net is obtained by unfolding: lay the bottom flat, unfold the four side faces out, and place the top opposite the bottom. It forms a cross or T-shape with 6 rectangles.
  3. 3
    Step 3: Calculate each pair's area: 2(5×3)=302(5 \times 3) = 30 cm², 2(5×2)=202(5 \times 2) = 20 cm², 2(3×2)=122(3 \times 2) = 12 cm².
  4. 4
    Step 4: Total surface area =30+20+12=62= 30 + 20 + 12 = 62 cm².

Answer

Total surface area =62= 62 cm²
A net is the 2D unfolding of a 3D figure. For a rectangular prism, the net has 6 rectangles. Adding their areas (which is the total surface area) gives 62 cm². Nets make surface area calculation visually intuitive.

About Nets

A net is a two-dimensional layout of all the faces of a three-dimensional solid, arranged so that folding along the edges produces the original solid. Nets reveal the surface area as the sum of flat face areas.

Learn more about Nets →

More Nets Examples

Example 2 medium

Describe the net of a regular triangular pyramid (tetrahedron with equilateral triangle faces) with

Example 3 easy

How many faces does a triangular prism have, and what shapes are they? If the triangular base has ba

Example 4 hard

A cylindrical can has radius [formula] cm and height [formula] cm. Describe its net and find the tot

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