The total surface area of the regular octahedron is approximately 152.46 square inches.
The formula for the surface area of a regular octahedron in terms of the area of its faces is:
Surface Area = 2× √3 ×Area of one face × Number of faces
For an octahedron, there are 8 faces in total. Given that the area of each face is 5.5 in^2 :
Surface Area = 2× √3 ×5.5in 2 ×8
Let's calculate:
Surface Area = 2× √3 ×5.5×8
Surface Area = 2×√3 ×44
Surface Area ≈ 152.46in^2
Therefore, the total surface area of the regular octahedron is approximately 152.46 square inches.
Question
Find the total area (surface area) of a regular octahedron if the area of each face is 5.5 in^2.