Nets Math Example 2

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Example 2

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Describe the net of a regular triangular pyramid (tetrahedron with equilateral triangle faces) with edge length 66 cm. Find its total surface area using the net.

Solution

  1. 1
    Step 1: A regular tetrahedron has 4 congruent equilateral triangular faces. Its net consists of one central equilateral triangle with three more equilateral triangles hinged to each of its three sides (a pinwheel/clover layout).
  2. 2
    Step 2: Find the area of one equilateral triangle with side 66 cm: A△=34s2=34(6)2=3634=93A_{\triangle} = \frac{\sqrt{3}}{4}s^2 = \frac{\sqrt{3}}{4}(6)^2 = \frac{36\sqrt{3}}{4} = 9\sqrt{3} cm².
  3. 3
    Step 3: Total surface area =4×93=363≈62.35= 4 \times 9\sqrt{3} = 36\sqrt{3} \approx 62.35 cm².
  4. 4
    Step 4: The net visually confirms that all four faces are congruent, making it easy to count and compute: multiply one face's area by 4.

Answer

Net: 4 equilateral triangles; SA=363≈62.35SA = 36\sqrt{3} \approx 62.35 cm²
The net of a regular tetrahedron is 4 equilateral triangles arranged in a row or pinwheel pattern. Each has area (√3/4)(36) = 9√3 cm², and the total surface area of all four faces is 36√3 cm².

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 →

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