Page 158 - NUMINO Challenge_D1
P. 158
Problem solving Creative Thinking p.82~p.83
1 A triangular prism has 5 faces, 9 edges, and 6 1
vertices. The numbers of faces, edges, and Equilateral triangle Rectangle with Rhombus Regular hexagon
vertices of the cut-out solid figure increase by 1, with the the largest area
3, and 2, respectively, so that the cut-out figure
has 6 faces, 12 edges, and 8 vertices. largest area
2 The upper part is a pentagonal pyramid and the Answers will vary.
lower part is the frustum of a pentagonal 2
pyramid. The pentagonal pyramid has 6 faces,
10 edges, and 6 vertices. The frustum of a 3 The two cut-out solid figures have the same
pentagonal pyramid has 7 faces, 15 edges, and
10 vertices. So they have 13 faces, 25 edges, shape. There are 15 edges in one of the solid
and 16 vertices. figures, so the sum of the number of edges is 15
2 30.
4 The 8 faces of a regular octahedron are cut into 8
regular hexagons. There are 6 squares in the
locations of the original vertices. The 12 original
edges still exist, but have a reduced length. At
every location of the original vertex, 4 new edges
are created. Therefore, the total number of
edges is 12 4 6 36. At every location of the
original vertex, there are 4 new vertices instead
of the original one, so there are 6 4 24
vertices. Therefore, the solid figure has 14 faces,
36 edges, and 24 vertices.
Answer Key
1 A triangular prism has 5 faces, 9 edges, and 6 1
vertices. The numbers of faces, edges, and Equilateral triangle Rectangle with Rhombus Regular hexagon
vertices of the cut-out solid figure increase by 1, with the the largest area
3, and 2, respectively, so that the cut-out figure
has 6 faces, 12 edges, and 8 vertices. largest area
2 The upper part is a pentagonal pyramid and the Answers will vary.
lower part is the frustum of a pentagonal 2
pyramid. The pentagonal pyramid has 6 faces,
10 edges, and 6 vertices. The frustum of a 3 The two cut-out solid figures have the same
pentagonal pyramid has 7 faces, 15 edges, and
10 vertices. So they have 13 faces, 25 edges, shape. There are 15 edges in one of the solid
and 16 vertices. figures, so the sum of the number of edges is 15
2 30.
4 The 8 faces of a regular octahedron are cut into 8
regular hexagons. There are 6 squares in the
locations of the original vertices. The 12 original
edges still exist, but have a reduced length. At
every location of the original vertex, 4 new edges
are created. Therefore, the total number of
edges is 12 4 6 36. At every location of the
original vertex, there are 4 new vertices instead
of the original one, so there are 6 4 24
vertices. Therefore, the solid figure has 14 faces,
36 edges, and 24 vertices.
Answer Key
