1. Lesson 1 – 7 Three-Dimensional Figures
Geometry
Lesson 1 – 7
Three-Dimensional Figures
Objective:
Identify and name three-dimensional figures.
Find surface area and volume.

2. Polyhedrons Polyhedrons Face – each flat surface
A solid with all flat surfaces that enclose a single region of space.
Face – each flat surface
Edges – the line segment where the faces intersect
Vertex – the point where 3 or more edges intersect

3. Types of Solids: Prism
A polyhedron with 2 parallel and congruent faces called bases
Bases are connect by parallelogram faces
This is one example of a prism
Named using the bases:
Pentagonal Prism

4. Naming Prisms
Triangular
Prism
Rectangular
Prism

5. Types of Solids: Pyramid
A polyhedron that has a polygonal base and three or more triangular faces that meet at a common point.
One example:
Rectangular Pyramid

6. Naming Pyramids Triangular Rectangular Pyramid Pyramid Pentagonal

7. Types of Solids: Cylinder
Not a polyhedron
A solid with congruent parallel circular bases connected by a curved surface.

8. Types of Solids: Cone Not a polyhedron
A solid with a circular base connected by a curved surface to a single vertex.

9. Types of Solids: Sphere
Not a polyhedron
A set of points in space that are the same distance from a given point. A sphere has no faces, edges, or vertices.

10. Determine whether the solid is a polyhedron, if yes, name the bases, faces, edges, and vertices.
Yes a polyhedron
Bases: MNOP & RSTQ
*Use the ‘top’ and ‘bottom’ on
Rectangular prisms for the bases.
Faces: MNOP, RSTQ,
MRQP, RSNM, STON, PQTO
Remember to include the bases
Edges:
Vertices: R, M, S, N, T, O, Q, P

11. Determine whether the solid is a polyhedron, if yes, name the bases, faces, edges, and vertices.
Not a polyhedron

12. Determine whether the solid is a polyhedron, if yes, name the bases, faces, edges, and vertices.
Bases: GHI & JKL
Faces: GHKJ, HKLI, & GJLI
Vertices: G,H,K,J,L,I

13. Regular Polyhedron
A polyhedron with all faces regular polygons and all edges congruent.
Can you think of a regular polygon?

14. Regular Polyhedrons: Platonic Solids

15. Regular Polyhedrons: Platonic Solids

16. Area & Volume
Lateral Area – area of the lateral faces (faces that are not bases)
Surface Area (Total Area)– is the area of the whole figure
Lateral area + area of bases
Volume – the measure of the amount of space enclosed by a solid figure.

17. Hands-on Activity Using the geometric solids set
Find formulas for the following for all solids
Lateral Area
Surface Area (Total Area)
Volume

18. Find Surface area and Volume
Square Pyramid
Surface area (Total Area): write formula first
Find P and B first
P = 4(6) = 24
= 96 cm2
B = 6*6 = 36
Plug into formula
Continued…

19. Continued…Volume
Remember B = 36
= 48 cm3

20. Find Surface area & Volume
Need to have both!
Need to have both!

21. Find Surface Area & Volume
P = 2(5.2) + 2(10) = 30.4
B = (5.2)(10) = 52
T = (30.4)(6) + 2(52)
V = Bh
= cm2
= (52)(6)
= 312 cm3

22. Find the Surface Area & Volume
rounded up
rounded up to

23. The diameter of the pool Mr. Sato purchased is 8 feet
The diameter of the pool Mr. Sato purchased is 8 feet. The height of the pool is 20 inches. Find each measure to the nearest tenth.
Surface Area of pool
*Be careful dealing with feet and inches!
We don’t need 2 bases since the pool
Does not have a top
20 inches is 1 2/3 feet

24. Volume of water needed to fill the pool to a depth of 16 inches.
Be careful with feet and inches!
16 inches is 1 1/3 feet