This 8-sided octahedron is a composite figure consisting of 2 square pyramids. The base of the pyramid is 33 mm, and the slant height is 28.6 mm.What is the surface area of the octahedron?

To solve this problem you must apply the proccedure shown below:

 1. You have that the 8-sided octahedron is a composite figure consisting of 2 square pyramids. Therefore, you must apply the formula for calculate the area of a square pyramid, which is:

 A=s²+2sl

 A is the area of the square pyramid.
 s is the base of the square pyramid (s=33 mm).
 l is slant height od the square pyramid (l=28.6 mm).

 2. Then, when you susbtitute these values into the formula shown above, you obtain:

 A=s²+2sl
 A=(33 mm)²+2(33 mm)(28.6 mm)
 A=1089 mm²+1887.6 mm²
 A=2,976.6 mm²

 3. Therefore, the area of the surface area of the octahedron is:

 SA=2A
 SA=2(2,976.6 mm²)
 SA=5,953.2 mm²

 The answer is: 5,953.2 mm²