12.1 & 12.2 – Explore Solids & Surface Area of Prisms and Cones

Polyhedron: A solid that is bounded by polygons

Faces: Polygon on the side of the shape Ex: Hex ABCDFE Quad EFKL

Edges: Where two polygons meet to form a line Ex:

Vertex: Where 3 polygons meet to form a point Ex:

Non-Polyhedron: An edge that isn’t a polygon

Base:Polygon the solid is named after.

Lateral Faces: Parallelograms or triangles on the sides of the solid

Prism: Polyhedron with two parallel, congruent bases Named after its base

Pyramid: Polyhedron with one base and lateral faces Named after its base.

Regular: All of the faces are congruent regular polygons

Convex: Any two points on its surface can be connected by a segment that lies entirely inside or on the solid

Concave: A side of the solid goes inward

Cross Section: Intersection of a plane and a solid

Euler’s Theorem: Faces + Vertices = Edges + 2 F + V = E + 2

Platonic Solids: Regular Polyhedra, only 5. Named after how many faces they have

Regular Tetrahedron: 4 faces

Cube: 6 faces

Regular Octahedron: 8 faces

Regular Dodecahedron: 12 faces

Regular Icosahedron: 20 faces

Determine whether the solid is a polyhedron. If it is, name the polyhedron and state the number of faces, vertices, and edges. Rectangular prism Polyhedron: YES or NO Faces: ___________ Vertices: _________ Edges: ___________ F + V = E = = 14

Determine whether the solid is a polyhedron. If it is, name the polyhedron and state the number of faces, vertices, and edges. curved sides Polyhedron: YES or NO Faces: ___________ Vertices: _________ Edges: ___________

Determine whether the solid is a polyhedron. If it is, name the polyhedron and state the number of faces, vertices, and edges. Pentagonal Pyramid Polyhedron: YES or NO Faces: ___________ Vertices: _________ Edges: ___________ F + V = E = = 12

Determine whether the solid is a polyhedron. If it is, name the polyhedron and state the number of faces, vertices, and edges. Triangular prism Polyhedron: YES or NO Faces: ___________ Vertices: _________ Edges: ___________ F + V = E = = 11

Determine whether the solid is a polyhedron. If it is, name the polyhedron and state the number of faces, vertices, and edges. curved side Polyhedron: YES or NO Faces: ___________ Vertices: _________ Edges: ___________

Use Euler’s Theorem to find the value of n. F + V = E + 2 n + 8 = n + 8 = 14 n = 6

Use Euler’s Theorem to find the value of n. F + V = E = n = n = n

Use Euler’s Theorem to find the value of n. F + V = E n = n = 20 n = 12

Sketch the polyhedron. Cube

Sketch the polyhedron. Rectangular prism

Sketch the polyhedron. Pentagonal pyramid

Determine if the solid is convex or concave. convex

Determine if the solid is convex or concave. concave

Determine if the solid is convex or concave. convex

Describe the cross section formed by the intersection of the plane and the solid. pentagon

Describe the cross section formed by the intersection of the plane and the solid. circle

Describe the cross section formed by the intersection of the plane and the solid. triangle

Cylinder: Prism with circular bases

Surface area: Area of each face of solid

Lateral area: Area of each lateral face

Right Prism: Each lateral edge is perpendicular to both bases

Oblique Prism: Each lateral edge is NOT perpendicular to both bases

Net: Two-dimensional representation of a solid

Surface Area of a Right Prism: SA = 2B + PH B = area of one base P = Perimeter of one base H = Height of the prism H

Surface Area of a Right Cylinder: H SA = 2B + PH

1. Name the solid that can be formed by the net. Cylinder

1. Name the solid that can be formed by the net. Triangular prism

1. Name the solid that can be formed by the net. rectangular prism Cube?

2. Find the surface area of the right solid. SA = 2B + PH SA = 2(30) + (22)(7) B = bh B = (5)(6) B = 30 P = P = 22 SA = SA = 214m2m2

2. Find the surface area of the right solid. SA = 2B + PH SA = 2(30) + (30)(10) P = P = 30 SA = SA = 360cm 2 c 2 = a 2 + b 2 c 2 = (5) 2 + (12) 2 c 2 = c 2 = 169 c = 13

2. Find the surface area of the right solid. cm 2

2. Find the surface area of the right solid. in 2 144in

3. Solve for x, given the surface area. SA = 2B + PH 142 = 2(5x) + (2x + 10)(7) B = bh B = 5x P = 5 + x x P = 2x = 10x + 14x = 24x = 24x 3ft = x

3. Solve for x, given the surface area.