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Answers to Check Your Work<br />
3. He can make three different models:<br />
The first one is a pyramid with a<br />
triangular base with sides of 5 cm.<br />
The other three edges are 10 cm.<br />
10 cm<br />
5 cm<br />
The second model is also a pyramid<br />
with a triangular base, but now all<br />
edges of the pyramid are 5 cm.<br />
The third possible model is a prism.<br />
The top <strong>and</strong> bottom faces are triangles<br />
with sides of 5 cm, <strong>and</strong> the edges of<br />
the rectangles are 10 cm.<br />
5 cm<br />
5 cm<br />
5 cm<br />
10 cm<br />
Note that a pyramid with a triangular<br />
base with sides of 10 cm is not possible!<br />
4. a. The prism has eight faces in total. Four faces are hidden.<br />
b. Two vertices are hidden.<br />
c. Six faces have the shape of a rectangle.<br />
d.<br />
e. Faces: 8; vertices: 12; edges: 18.<br />
f. Hint: To find the number of diagonals in the<br />
top face, you can draw the shape <strong>and</strong> find all<br />
diagonals. Count them while you are drawing!<br />
The total number of face diagonals of the<br />
prism is 30. The top <strong>and</strong> bottom face have<br />
nine diagonals each (2 9), <strong>and</strong> the other<br />
faces have two diagonals each (6 2), so<br />
in total: 6 2 2 9 30 diagonals.<br />
Answers to Check Your Work 61
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