1. 9. 1 Obj: Identify polyhedrons and identify their faces & bases
9.1 Obj: Identify polyhedrons and identify their faces & bases. EQ: What are the names of solid figures & how many faces, bases and edges do they have?

2. Polyhedron
3-D shape made up of polygons (triangles, quadrilaterals, pentagons, hexagons, etc.)
Notes
a circle is not a polygon
No curved sides

3. Types of Solids

4. A cylinder has a curved surface, so it is not a polyhedron.
Example 1
Identify and Name Polyhedra
Tell whether the solid is a polyhedron. If so, identify the shape of the bases. Then name the solid. a. b.
SOLUTION a.
The solid is formed by polygons so it is a polyhedron. The bases are congruent triangles in parallel planes. This figure is a triangular prism. b.
A cylinder has a curved surface, so it is not a polyhedron.

5. Naming Polyhedrons Identify Shape: Pyramid or Prism???
Comes to a point
Only one base
Prism
Two bases
2. Name shape by its base.

6. Use the diagram at the right.
Example 2
Find Faces and Edges
Use the diagram at the right.
Name the polyhedron. a.
Count the number of faces and edges. b.
List any congruent faces and congruent edges. c.
SOLUTION
The polyhedron is a hexagonal pyramid. a.
The polyhedron has 7 faces and 12 edges. b.
Using the markings on the diagram, you can conclude the following: c.

7. Example 2 Congruent faces ∆PQV  ∆QRV  ∆RSV Congruent edges QR PQ ST
Find Faces and Edges
Congruent faces
∆PQV  ∆QRV  ∆RSV
Congruent edges QR PQ ST RS TU  UP
∆STV  ∆TUV  ∆UPV PV QV SV RV TV  UV

8. Draw the triangular bases. 1. Sketch a triangular prism.
Example 3
Sketch a Polyhedron
SOLUTION
Draw the triangular bases. 1.
Sketch a triangular prism.
Connect the corresponding vertices of the bases with vertical lines. 2.
Partially erase the hidden lines to create dashed lines. Shade the prism. 3.

9. Checkpoint
Identify and Sketch Polyhedra
Tell whether the solid is a polyhedron. If so, identify the shape of the base(s). Then name the solid. 1.
ANSWER
yes; triangular;
triangular prism 2.
ANSWER
no; cone 3.
ANSWER
yes; rectangular;
rectangular pyramid

10. Draw a rectangular pyramid.

11. Draw a rectangular pyramid.

12. Draw a rectangular pyramid.

13. Draw a rectangular pyramid.

14. Draw a rectangular pyramid.

15. Draw a rectangular pyramid.

16. Draw a rectangular pyramid.

17. Checkpoint
Identify and Sketch Polyhedra
Copy the partial drawing of a triangular pyramid. Then complete the drawing of the pyramid. 4.
ANSWER

18. 1.
Find the circumference and area of the circle.
Round your answers to the nearest whole number.
a circle with a radius of 3 inches
circumference: 19 in.; area: 28 in.2
ANSWER 2.
a circle with a diameter of 13 meters
circumference: 41 m; area: 133 m2
ANSWER

19. 3.
Find the area of the shaded sector. Start by finding the area of the circle. Round your answer to the nearest whole number.
177 m2
ANSWER 4.
A circular swimming pool has a circumference of 63 feet. What is the radius of the pool, to the nearest foot?
10 ft
ANSWER

20. Worksheet 9.1B