1. PRISMS The two shaded faces of the prism shown are its bases.

Slides:

Advertisements

Similar presentations

Surface Area of Prisms and Cylinders Section 12.2

Advertisements

Chapter 12 – Surface Area and Volume of Solids

Congruent Two shapes that are the same size and shape

7.G.6 Surface Areas of Prisms and Cubes Objective 7.G.6 – Find the surface area of prisms.

PRISMS AND CYLINDERS: VOLUMES, SURFACE AREAS, AND WEIGHTS

Prisms Lesson 9-2.

Honors Geometry Sections 6.3 & 7.2 Surface Area and Volume of Prisms

Lateral Area, Surface Area, and Notes

3.2a: Surface Area of Prisms and Cylinders

Section 12-1 Prisms. Prism a 3-dimensional figure with two congruent, parallel faces The congruent, parallel faces are called the bases. The bases lie.

12-2 Surface Area of Prisms You found areas of polygons. Find lateral areas and surface areas of prisms. Find lateral areas and surface areas of cylinders.

INTRODUCTION: A polyhedron is a geometric figure made up of a finite number of polygons that are joined by pairs along their sides and that enclose a.

Bell Work: Use substitution to solve for x and y: x – 2y = -1 2x – 3y = 4.

Geometric Solids: The Prism. 2 Review of Planes A plane is a flat surface (think tabletop) that extends forever in all directions. It is a two-dimensional.

The two shaded faces of the prisms shown are its bases An altitude of a prism is a segment joining the two base planes and perpendicular to both The faces.

Surface Area and Volume

Ch 11-4 Surface Area of A Prism C. N. Colón St. Barnabas HS Geometry.

Chapter 12 Notes.

Jeopardy 20 Squares Start.

Prisms Prism – Every prism has two congruent faces which are polygonal regions and lie in parallel planes. These polygonal regions are called bases.

The area of a rectangle equals its length times the width (base times the height). A = length x width = lw or A = base x height = bh Area of a Rectangle.

Prisms Lesson 11-2.

OBJECTIVE AFTER STUDYING THIS SECTION, YOU WILL BE ABLE TO FIND THE SURFACE AREAS OF PRISMS 12.1 Surface Areas of Prisms.

Chapter 12 Notes: Surface Area and Volume of Prisms Goal: Students will find the surface area and volume of prisms.

GeometryMrs. McConaughy1 Prisms and Pyramids Objectives: To define and illustrate prisms, pyramids, and their parts.

Chapter 10: Surface Area and Volume

Chapter 11: Surface Area & Volume

CHAPTER 12 AREAS AND VOLUMES OF SOLIDS 12-1 PRISMS.

Lesson 12.1 Exploring Solids Today, we will learn to… > use vocabulary associated with solids > use Euler’s Formula.

Identify each of the following shapes. In geometry, what is a net? what is surface area? cube Triangular pyramid Right square pyramid Rectangular prism.

Areas and Volumes of Prisms

Warm Up Classify each polygon. 1. a polygon with three congruent sides 2. a polygon with six congruent sides and six congruent angles 3. a polygon with.

Gaby Pavia and Gaby Pages. Section 12-1 Bases: congruent polygons lying in parallel planes Altitude: segment joining the two base planes and perpendicular.

11.2 Surface Area of Prisms & Cylinders Prism Z A polyhedron with two congruent faces (bases) that lie in parallel planes. The lateral faces are parallelograms.

11-1 Space Figures and Cross Sections. Polyhedra A polyhedron is a three- dimensional figure whose surfaces are polygons. Each polygon is a face of the.

10-3 Surface Areas of Prisms

10.3 – Surface Areas of Prisms and Cylinders. Warm Up.

11.2 Surface Area of Prisms and Cylinders. Prism - a polyhedron with exactly 2 congruent, parallel faces, called bases. (base shape names the prism) Lateral.

Warm Up Classify each polygon. 1. a polygon with three congruent sides 2. a polygon with six congruent sides and six congruent angles 3. a polygon with.

Geometry 12.1 Prisms. Today you will learn how to find three measurements about prisms. You will find: Prisms Lateral area: L.A. Total area: T.A. Volume:

Chapter 10 Notes Area: Parallelograms Area of a figure is the number of square units it encloses. The stuff inside of a figure. Area of a Parallelogram:

Group 6 Period 5 Problems Mac Smith, Jacob Sweeny Jack McBride.

Chapter 12 Group 6 P Crowley C Prince C King K Connell.

Prisms Unit 12 Section 1 Identify the parts of prisms Find the lateral areas, total areas, and volumes of right prisms.

Opener. UNIT EQ: HOW DO YOU CALCULATE THE SURFACE AREA AND VOLUME OF A 3-DIMENSIONAL FIGURE Surface Area & Volume.

How to find the surface area of a prism and cylinder. Chapter 11.2GeometryStandard/Goal 2.2.

Chapter Surface Area of Prisms and Cylinders Find the surface area of a prism Find the surface area of a cylinder.

Volume of Rectangular Prisms EQ: How do you find the volume of rectangular prisms?

Section 12-3 Cylinders. cylinder It is like a prism except that its bases are circles instead of polygons. Bases.

Chapter 12 Areas and Volumes of Solids (page 474) Essential Question How can you calculate the area and volume of any solid?

 A Prism is a polyhedron with two congruent, parallel bases.  The other faces are lateral faces.  A prism is named for the shape of its bases.

Part 1 Polygons Triangles A triangle is a polygon with 3 sides. VERTEX SIDE A=1/2bh or A=bh/2.

Section 12-2 Pyramids.

Part 1 Polygons.

Lesson 21.1: Volume of Prisms and Cylinders

square rectangle triangle pentagon rhombus

12.2 Surface Area of Prisms & Cylinders

AREA AND VOLUME Form 1 Mathematics Chapter 7.

11.2 Surface area of prisms and cylinders

10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

Lateral Area &Surface Area Of Prisms

Warm Up Classify each polygon. 1. a polygon with three congruent sides

9.4 – Perimeter, Area, and Circumference

12.2 Surface Area of Prisms & Cylinders

A prism is a polyhedron with two parallel faces called bases.

Geometry: Chapter 9 9.2: Surface Area and Volume of PRISMS

Volume of Prisms, Cross Sections and Scale Factors

9.1 Prisms, Area, & Volume 8/7/2019 Section 9.1 Nack/Jones.

Presentation transcript:

1. PRISMS The two shaded faces of the prism shown are its bases. The bases are congruent polygons lying in parallel planes. home

home

The faces of a prism that are not its bases are called lateral faces. The lateral faces of a prism are parallelograms. If they are rectangles, the prism is a right prism. Otherwise the prism is an oblique prism. home

The diagrams below show that a prism is also classified by the shape of its bases. Right triangular prism Right rectangular prism (Rectangular solid) Oblique pentagonal prism Lateral edge is not an altitude Lateral edges are altitudes home

Lateral Area and Total Area of a Prism The lateral area (L.A.) of a prism is the sum of the areas of its lateral faces. The total area (T.A.) is the sum of the areas of all its faces. home

Lateral Area and Total Area of a Prism The right pentagonal prism can be used to illustrate the development of the lateral area formula: L.A. = ah+bh+ch+dh+eh = (a+b+c+d+e)h = perimeter • h = ph home

home

Lateral Area and Total Area of a Prism The Method applies to any right prism. The lateral area equals the perimeter of a base times the height of the prism. (L.A. = ph) home

Prisms have volume as well as area Prisms have volume as well as area. A rectangular solid with square faces is a cube. Since each edge of the blue cube shown is 1 unit long, the cube is said to have a volume of 1 cubic unit. The larger rectangular solid has 3 layers of cubes, each layer containing (4•2) cubes. Hence its volume is (4•2)•3, or 24 cubic units. Volume = Base area x height home

home

The Volume of a Right Prism The same sort of reasoning is used to find the volume of any right prism. The volume of a right prism equals the area of a base times the height of the prism. (V = Bh) home

Example 1 A right trapezoidal prism is shown. Find the lateral area, total area, volume. home

home

Example 2 A right triangular prism is shown. The volume is 315. Find the total area. home

home

Example 3 The container shown has the shape of a rectangular solid. When a rock is submerged, the water level rises 0.5 cm. Find the volume of the rock. home

home

Example 4 A right prism has square bases with edges that are three times as long as the lateral edges. The prism's total area is 750 m2. Find the volume. home

The Volume of an Oblique Prism The volume of an oblique prism equals the area of a base times the height of the prism or right cross-section area times the length of the lateral edge. home

home

The Volume of an Oblique Prism Volume = Base Area x Altitude = Right Cross-section Area x Length of lateral edge home

Example 5 The oblique square prism shown has base edge 3. A lateral edge that is 15 makes a 60° angle with the plane containing the base. Find the exact volume. home

home

Example 6 In the parallelepiped ABCD, right cross-section area is a square with sides 1 cm. If =60° and cm, find the volume of the prism. home

home

Note A diagonal of a right rectangular prism joins two vertices not in the same face. The length of the diagonals is home

home

If the diagonals of a cube are cm long, what is the volume? Example 7 If the diagonals of a cube are cm long, what is the volume? home