Question

fill in the blank under each figure below. triangular prism octahedron tetrahedron number of faces = number of edges = number of vertices =

Explanation:

Step1: Count faces of triangular prism

A triangular prism has 2 triangular bases and 3 rectangular lateral - faces. So, the number of faces is $2 + 3=5$.

Step2: Count edges of octahedron

An octahedron has 12 edges. We can visualize it or use Euler's formula $V - E+F = 2$ (where $V$ is vertices, $E$ is edges and $F$ is faces). For an octahedron, $F = 8$ and $V=6$, then $6 - E+8 = 2$, solving for $E$ gives $E = 12$.

Step3: Count vertices of tetrahedron

A tetrahedron has 4 vertices. It is a 3 - D shape with 4 triangular faces and 4 vertices.

Answer:

Number of faces (triangular prism) = 5
Number of edges (octahedron) = 12
Number of vertices (tetrahedron) = 4