Find the surface area and volume of a regular tetrahedron of side 10cm.

1 answer

A regular tetrahedron is a polyhedron with four congruent equilateral triangles as its faces.

To find the surface area of a regular tetrahedron, we need to find the area of each of its four equilateral triangles and add them up. The formula for the area of an equilateral triangle is A = (s^2 * sqrt(3))/4, where s is the side length.

Area of one equilateral triangle = (10^2 * sqrt(3))/4 = 25sqrt(3) cm^2
Total surface area = 4 * 25sqrt(3) = 100sqrt(3) cm^2

To find the volume of a regular tetrahedron, we can use the formula V = (s^3 * sqrt(2))/12, where s is the side length.

Volume = (10^3 * sqrt(2))/12 = 100sqrt(2)/12 = 50sqrt(2)/6 = 25sqrt(2)/3 cm^3

Therefore, the surface area of the regular tetrahedron is 100sqrt(3) cm^2 and the volume is 25sqrt(2)/3 cm^3.