GeometryLesson 1 – 7

Three-Dimensional Figures

Objective:Identify and name three-dimensional figures.

Find surface area and volume.

PolyhedronsPolyhedronsA 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

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

Naming Prisms

Triangular Prism

RectangularPrism

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

Naming Pyramids

TriangularPyramid

RectangularPyramid

PentagonalPyramid

Types of Solids:Cylinder

Not a polyhedron

A solid with congruent parallel circular bases connected by a curved surface.

Types of Solids:Cone

Not a polyhedron

A solid with a circular base connected by a curved surface to a single vertex.

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.

Determine whether the solid is a polyhedron, if yes, name the bases,

faces, edges, and vertices.

Yes a polyhedronBases: MNOP & RSTQ

*Use the ‘top’ and ‘bottom’ on Rectangular prisms for the bases.

Faces: MNOP, RSTQ, MRQP, RSNM, STON, PQTO

Edges: QPTOSNRM

RQMPPOQTNOSTRSMN

Vertices: R, M, S, N, T, O, Q, P

Remember to include the bases

Determine whether the solid is a polyhedron, if yes, name the bases,

faces, edges, and vertices.

Not a polyhedron

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

Regular Polyhedron

A polyhedron with all faces regular polygons and all edges congruent.

Can you think of a regular polygon?

Regular Polyhedrons:Platonic Solids

Regular Polyhedrons:Platonic Solids

Area & VolumeLateral Area – area of the lateral faces (faces that are not bases)

Surface Area (Total Area)– is the area of the whole figureLateral area + area of bases

Volume – the measure of the amount of space enclosed by a solid figure.

Hands-on Activity

Using the geometric solids set

Find formulas for the following for all solidsLateral AreaSurface Area (Total Area)Volume

Find Surface area and Volume

Square Pyramid

Surface area (Total Area): write formula first

BPT 2

1

365242

1TFind P and B first

P = 4(6) = 24B = 6*6 = 36

Plug into formula

= 96 cm2

Continued…

Continued…Volume

BhV

3

1

Remember B = 36

4363

1V

= 48 cm3

Find Surface area & Volume 222 rrhT

2621862

hrV 2 186 2

72216 2288 cm

28.904 cmNeed to have both! 648

38.2035 cmNeed to have both!

Find Surface Area & Volume

BPhT 2P = 2(5.2) + 2(10) = 30.4B = (5.2)(10) = 52

T = (30.4)(6) + 2(52)= 286.4 cm2 V = Bh

= (52)(6)= 312 cm3

Find the Surface Area & Volume

2rrT 2151715

225255 2480 in

20.1508 in1507.96 rounded up to 1508.0

hrV 2

3

1

8153

1 23600 in

30.1885 in1884.95 rounded up

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

222 rrhT

243

2142

*Be careful dealing with feet and inches!

20 inches is 1 2/3 feet

163

113

insq

insq

2.923

129

We don’t need 2 bases since the pool Does not have a top

Volume of water needed to fill the pool to a depth of 16 inches.

hrV 2Be careful with feet and inches!

3

114 2V 16 inches is 1 1/3 feet

ftcubic

ftcubic

0.673

121