Question

use the solid figure to determine whether each statement is true or false. a. it is a polyhedron. b. it has 5 faces. c. the base is a rectangle. d. the lateral faces are rectangles. e. there are 6 vertices. f. there are 6 edges.

Explanation:

Step1: Define polyhedron

A polyhedron is a 3 - D shape with flat polygonal faces, straight edges and sharp vertices. The given figure meets these criteria, so "It is a polyhedron" is True.

Step2: Count faces

By observing the figure, we can count 2 triangular faces and 3 rectangular faces, totaling 5 faces. So "It has 5 faces" is True.

Step3: Identify base

The base of the given prism is a triangle, not a rectangle. So "The base is a rectangle" is False.

Step4: Check lateral faces

The lateral faces are rectangles. So "The lateral faces are rectangles" is True (assuming there was a mis - mark in the original answer for this part in the provided image).

Step5: Count vertices

Vertices are the corner - points. Counting them, we find there are 6 vertices. So "There are 6 vertices" is True.

Step6: Count edges

Edges are the line - segments where faces meet. Counting them, we find there are 9 edges, so "There are 6 edges" is False.

Answer:

a. True
b. True
c. False
d. True
e. True
f. False