Chapter 12.1, Problem 17PPS

a.

To determine

To draw: a pyramid and label it.

Explanation of Solution

Draw:

  

b.

To determine

To identify: the bases, faces and edges.

Explanation of Solution

  $\begin{array}{l}\text{Base = ABCD}\\ \text{Faces = AEB , BEC , AED , CED}\\ \text{Edges = AB , BC , CD , DA , BE , CE , DE , AE}\end{array}$

c.

To determine

To draw:To draw and describe the shape resulting from a vertical, angled, horizontal cross section of a pyramid.

Explanation of Solution

VERTICAL:

  

A vertical plane will cut the pyramid into two parts with the cross section of a triangle.

ANGLED:

  

An angled plane will cut the pyramid into two parts with the cross section of a trapezoid.

HORIZONTAL:

  

A horizontal plane will cut the pyramid into two parts with the cross section of a square.

d.

To determine

To draw: To draw and describe the shape resulting from the top and the base of a cross section of a pyramid.

Explanation of Solution

A plane at an angle relative to the top and the base that intersects the base of a rectangular pyramid makes a cross section which has one pair of parallel sides and one pair of non parallel sides.So,this cross section is a trapezoid.