Show me how to find the surface area of a tetrahedron when the sketch of the net of the tetrahedron on paper shows four congruent equilateral triangles each with a base of 5 inches and a height of approximately 4.33 inches. What should I do next? I need to find the surface area of this tetrahedron

Answer 1

To find the surface area of a tetrahedron with equilateral triangles as its faces, you can use the formula:

Surface area = √3 * side length^2

In this case, the side length of each triangle is the base of 5 inches. Therefore, the surface area of each triangle is:

Surface area = √3 * 5^2
Surface area = √3 * 25
Surface area ≈ 43.30 in^2

Since there are four congruent equilateral triangles making up the tetrahedron, the total surface area of the tetrahedron is:

Total surface area = 4 * 43.30
Total surface area ≈ 173.20 in^2

Therefore, the surface area of the tetrahedron is approximately 173.20 square inches.