Question

A solid has faces that consist of 5 congruent squares and 4 congruent equilateral triangles. The solid has 9 vertices. How many edges does the solid have? (no image)
A.
16 edges
B.
18 edges
C.
20 edges
D.
22 edges

Answer 1

The answer is A. 16 edges

For most of the solid shapes, we can use Euler's polyhedron formula:
f + v - e = 2
f - the number of faces
v - the number of vertices
e - the number of edges

We know:
f = 5 + 4 = 9
v = 9
e = ?

So:
f + v - e = 2
9 + 9 - e = 2
18 - e = 2
18 = e + 2
e = 18 - 2
e = 16