Final answer:
The surface area of the regular tetrahedron is approximately 81.39 square inches.
Step-by-step explanation:
A tetrahedron is a three-dimensional shape with four equilateral triangular faces. In a regular tetrahedron, all four faces are congruent. To find the surface area of the tetrahedron, we need to determine the length of its sides. We can use the formula for the volume of a regular tetrahedron to find the length: V = (sqrt(2)/12) * s^3, where V is the volume and s is the length of the side. Since the volume is given as 100 cubic inches, we can solve for s and find that s is approximately 5.93 inches. Now that we know the length of the side, we can use the formula for the surface area of a regular tetrahedron: SA = sqrt(3) * s^2. Plugging in the value of s, we get SA ≈ 81.39 square inches.