Question

refer to the figure for exercises 14 - 16. 14. how many planes are shown in the figure? 15. which side of the cube is coplanar with plane p? 16. are points h, e, a, and b coplanar? explain.

Explanation:

Step1: Identify planes in cube

A cube has 6 faces which are planes. Also, there is the plane \(P\) shown below the cube. So in total, there are 7 planes.

Step2: Determine coplanar side

The side of the cube that is in the same plane as plane \(P\) is the bottom - face \(ABCD\) of the cube.

Step3: Check coplanarity of points

Points \(H\), \(E\), \(A\), and \(B\) are not coplanar. Points \(H\) and \(E\) are on the top - face of the cube, while points \(A\) and \(B\) are on the bottom - face. There is no single flat surface that can contain all four points.

Answer:

1. 7
2. Face \(ABCD\)
3. No. Points \(H\) and \(E\) are on top - face, \(A\) and \(B\) are on bottom - face, no single plane contains all four.