Question

A solid square-based pyramid has all of its corners cut off, as shown. How many edges does the resulting shape have?

a) 12
b) 16
c) 20
d) 24

Answer 1

A solid square-based pyramid with all its corners cut off results in an octahedron, which has 13 edges.

Step-by-step explanation:

A solid square-based pyramid with all its corners cut off results in a shape known as an octahedron. An octahedron has 8 faces, 6 corners, and 12 edges. To find the number of edges in the resulting shape, we add the edges of the original square-based pyramid to the edges created by cutting off the corners. The original pyramid has 8 edges, and each corner cut off introduces 3 new edges. Therefore, the resulting shape has 8 + (6 x 3) = 26 edges. However, since each of these edges is shared by two faces, we must divide by 2 to get the final answer. Therefore, the resulting shape has a total of 26 / 2 = 13 edges. So, the correct answer is not given in the options provided.