Chloe used 30 toothpicks as edges to make a model for a prism. How many sides did the base of her prism have? How many vertices?
To find the number of sides on the base of Chloe's prism, we need to analyze the relationship between the number of sides and the number of edges in a prism.
A prism has two identical polygonal bases connected by rectangular faces. The number of edges in a prism is the sum of the edges on the top and bottom bases, plus the number of edges connecting corresponding vertices on the bases. In this case, we have a model made of toothpicks, and the total number of toothpicks (edges) used is given as 30.
Let's assume the number of edges on each base is 'n.'
Since the prism has two identical bases, the total number of edges on the bases would be 2n.
Additionally, each vertex on the top base is connected to a corresponding vertex on the bottom base, adding 'n' more edges.
Hence, the total number of edges in the prism is: 2n + n = 3n.
We know that Chloe used a total of 30 toothpicks as edges for her prism.
So, 3n = 30. Dividing both sides by 3 gives us n = 10.
Therefore, the base of Chloe's prism has 10 sides.
To find the number of vertices, it's important to understand that the vertices of the top base align with the vertices of the bottom base.
Since each base has 'n' vertices, the total number of vertices in the prism would be 2n.
Substituting the value of 'n' as 10, we have 2 * 10 = 20.
Hence, Chloe's prism has 20 vertices.