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A solid regular octahedron has volume cubic inches. what is the surface area of the octahedron?

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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.

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