Please need help with geometry homework!

Question

Question 1: Identify the number of vertices, edges, and faces of the polyhedron. Use your results to verify Euler's formula.

A.) V = 8, E = 10, F = 4; 8 − 10 + 4 = 2

B.) V = 6, E = 10, F = 6; 6 − 10 + 6 = 2

C.) V = 8, E = 12, F = 6; 8 − 12 + 6 = 2

D.) V = 6, E = 12, F = 8; 6 − 12 + 8 = 2

Question 2: The edge length of a cube is 17 cm. Identify the length of its diagonal. Round to the nearest tenth, if necessary.

A.) 29.4 cm

B.) 17 cm

C.) 24 cm

D.) 34 cm

Question 3: Two people meet in the purple room on the fourth floor of a building. On departure, one person travels West 20 feet, South 12 feet, and Down 12 feet. The other person travels North 20 feet, East 10 feet, and Up 12 feet. How far apart are the two people? Round to the nearest tenth.

A.) 41.6 ft.

B.) 55.4 ft.

C.) 50 ft.

D.) 51.6 ft.

Question 4: Do the orthographic views represent the object? Does the isometric view represent the object? (Assume there are no hidden cubes.)

A.) yes, yes

B.) no, no

C.) no, yes

D.) yes, no

Question 5: Identify the distance between the points (9,7,3) and (5,3,2), and identify the midpoint of the segment for which these are the endpoints. Round to the nearest tenth, if necessary.

A.) d ≈ 17.9 units; M (2, 2, 0.5)

B.) d ≈ 5.7 units; M (7, 5, 2.5)

C.) d ≈ 5.7 units; M (2, 2, 0.5)

D.) d ≈ 17.9 units; M (7, 5, 2.5)

Question 6: Which of the following shows an accurate isometric view of the object?

Here are the options:

A.)

B.)

C.)

D.)

Please give explanations and answer for each question.

Answer 1

Problem Number One:

The faces of the polyhedron are the triangles that you can see on the outside of the shape. Imagine the polyhedron is a solid block that you can hold in your hand. You would see a triangle on the top and another on the bottom. Then when you look at one side of the block, you would see three triangles. When you turn it over, you would see three more. So in all, there are eight triangles, or eight faces on the polyhedron.

 An edge of this polyhedron is where the sides of two triangles meet. On one side of the polyhedron, you would see two nearly horizontal edges at the top, two nearly vertical edges in the middle, and one horizontal edge at the bottom. That's five edges. On the other side, you would see the same thing, but flipped, so that makes ten. There are also two edges on the sides of the shape, making a total of twelve.

 Now, the vertices are the pointy angles where the corners (or vertices) of the triangles meet. There are three of them on the top and three on the bottom, making a total of six.

 Euler's formula states that the sum of the number of faces (F) and the number of vertices (V) on a polyhedron is equal to the number of edges (E) plus two. This is shown in the formula F+V=E+2. This could also be written as V-E+F=2. So, if you plug in the numbers (V=6, E=12, F=8), you get 6-12+8=2. This is correct, and it demonstrates that Euler's formula is true.