11-1 Exploring 3D figures

I. Polyhedra – solids with all flat surfaces that are not open

SPHERE

CYLINDER

CONEPYRAMID

CUBE

PRISM

II. Prisms A polyhedron with two

congruent faces that are polygons contained in parallel lines

Parts of a prism

FACE

Faces — The flat surfaces of a solid object.

EDGE

Edges — the line segments where the faces intersect

BASEThe two congruent faces of a prism

LATERAL

FACE

The other faces of the prism which

connect the two bases.

LATERAL EDGES

Platonic Solids

III. Regular Polyhedra

All of its faces are shaped like congruent regular polygons

IV. Slices

V. Examples

1. Draw a top, left, front, and right view of this model.

2. Identify the solid. Name its bases, faces, edges, and vertices.

3. Identify the polyhedra. Name its bases, faces, edges, and vertices.

4. Miranda has a piece of foam that is shaped like a cone. She wants to make a decorative centerpiece for a table using the cone. However, she does not want the centerpiece to have a point, but wants the top of the centerpiece to be an oval shape. How should she cut the cone to get an oval top?

11-3 Surface Area Prism and Cylinder

I. Prisms Oblique: Tilted at an angle; neither vertical

nor horizontal

Right: altitude is the height

II. Types of right prisms

RECTANGULAR

HEXAGONAL

TRIANGULAR

III. RIGHT PRISM PARTS

IV. VARIABLES USED FOR PRISMS

B- BASE L- LATERAL AREA P- PERIMETER OF BASE H- HEIGHT OF PRISM

Lateral Area of a Right Prism

LA = P * H

V. FORMULAS

Surface Area of Right prism

SA = P * H + 2 B

Examples:

1. Find the L and SA of a right triangular prism with a height of 10 inches and a right triangular base with legs of 10 and 12 inches.

VI. Cylinders

2 BASES ARE

CIRCLES

HEIGHT

RADIUS

LA = 2 R H

Surface area of a cylinder

Example 2. Find the Lateral Area and the Surface Area.

11-4 Surface area Pyramids and Cones

BASE

FACE

HEIGHT

EDGES

SLANT

HEIGHT

S A = ½ * P * L + B

CONE

BASE IS A CIRCLE

HEIGHT

RADIUS

SLANT

HEIGHT