Question

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?

Answer 1

3775.2mm squared

Explanation

You find the area of each side and add all of them together. You divide by 2 for every triangle, and the slant height is never used.

Answer 2

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