# Chapter 10

### Mitch M.

## Section 10.1

## Formulas

## Area of a parallelogram To find the area of a parallelogram you multiply the base by the height. A=bh | ## Real Life Example This popcorn holder Is and example of a trapezoid and you could find its area. | ## Area of a trapezoid To find the area of a trapezoid you add the length of b1 to b1. After you have done that you multiply your answer by the height then by one half. A=1/2(b1+b2)h |

## Area of a parallelogram

A=bh

## Words to know

The base of a parallelogram is the length of any one of its sides.

The perpendicular distance between the base and the opposite side is the height of a parallelogram.

The base of a trapezoid are its two parallel sides.

The perpendicular distance between the bases is the height of a trapezoid.

b1-one of the two parallel lines on a trapezoid.b2- one of the two parallel lines on a trapezoid.

## Example of a parallelogram

Answer:

A=bh

A=12*16

A=192 cm squared

## Example of a Trapezoid

Answer:

A=1/2(b1+b2)h

A=1/2(8+10)6

A=9*6

A=54 inches squared

## Section 10.2

## Formulas

## Circumference of a circle To find the circumference of a circle you multiply the radius times pi then by 2. A=2*pi*r Another way to find the circumference is to multiply the diameter by pi. A=d*pi | ## Area of circle To find the area of a circle you multiply the radius squared by pi. A=pi*r^2 | ## Real Life Example If you broke this window you would be able to order a new one with all the dimensions. You find the area of a full circle window and then divide that in half. |

## Circumference of a circle

A=2*pi*r

Another way to find the circumference is to multiply the diameter by pi.

A=d*pi

## Words to know

Radius- The distance from the edge of a circle to the center

Diameter- The distance from one edge to another on a circle crossing through the center point.

Circumference- The distance around a circle.

## Example of Area of a Circle

Answer:

A=pi*r^2

A=3.14*10^2

A=314 in squared

## Example of Circumference

Answer:

C=pi*2r

C=3.14*2*5

C=31.4 inches

Answer:

C=pi*d

C= 3.14*10

C=31.4 inches

## Section 10.3

## Formulas

## Prism A prism is a polyhedron. Prisms have two congruent bases that lie in parallel planes. The other faces are rectangles. | ## Pyramid A pyramid is a polyhedron. Pyramids have one base. The other faces are triangles. | ## Cylinder A cylinder is a solid with two congruent circular bases that lie in parallel planes. |

## Prism

## Cone A cone is a solid with one circular base. | ## Sphere A sphere is a solid formed by all points in space that are the same distance from a fixed point called the center. |

## Words to Know

A polyhedron is a solid that is enclosed by polygons.

The polygons that form a polyhedron are called faces.

The segments where faces of a polygon meet are called.

A vertex is a point where three or more edges meet.

## Example

Answer:

Faces-6

Edges-12

Vertices-8

## Section 10.4

## Formulas

## Surface area of a prism To find the surface area of a prism you multiply the area of the base by two the you add that to the perimeter of the base multiplied by the height S=2B+Ph | ## Real Life example If you are painting a room you will need to find the lateral surface area to see how much paint is needed. | ## Surface Area of a Cylinder To find the surface area of a prism you multiply the area of the base by 2 then add that to the circumference multiplied by the height. S=2B+Ch |

## Surface area of a prism

S=2B+Ph

## Real Life example

## Words to Know

The surface area of a polyhedron is the sum of all the area of its faces.

## Example of Surface Area of a Prism

Answer:

S=2B+Ph

S=2(bh)+Ph

S=2(9*4)+30*6

S=72+180

S+252 feet squared

## Example of Surface Area of a Cylinder

Answer:

S=2B+Ch

S=2pi*r^2+2pi*r*h

S=2*3.14*2^2+3.14*2*2*5

S=87.92 centimeters squared

## Section 10.5

## Formulas

## Surface Area of a Pyramid To find the surface area of a pyramid you add the area of the base to the perimeter of the base multiplied by the slant height then multiplied by one half S=B+1/2Pl | ## Real Life If you wanted to find how much space the pyramids in Egypt take up you could do that by finding its volume. | ## Surface Area of a Cone To find the surface area of a cone you multiply pi times the radius squared then you add that too pi times the radius times the slant height. S=pi*r^2+pi*rl |

## Surface Area of a Pyramid

S=B+1/2Pl

## Real Life

## Words to Know

## Example of Surface Area of a Pyramid

Answer:

S=B+1/2Pl

S=13+1/2*17*11

S=13+93.5

S=106.5 meters squared

## Example of Surface Area of a Cone

Answer:

S=pi*r^2+pi*rl

S=3.14*4^2+3.14*4*5

S=50.24+62.8

S=113.04 centimeters squared

## Section 10.6

## Formulas

## Volume of a Prism To find the volume of a prism you multiply the area of the base by the height V=Bh | ## Real Life You could find out how much room this soda can takes up in your fridge by finding its volume. | ## Volume of a Cylinder To find the volume of a cylinder you multiply the area of the base by the height V=Bh |

## Real Life

## Words to Know

## Example of Volume of a Prism

Answer:

V=Bh

V=(7*9)5

V=315 inches cubed

## Example of Volume of a Cylinder

Answer:

V=Bh

V=(3.14*10)20

V=31.4*20

V=628 centimeters cubed

## Section 10.7

## Formulas

## Volume Of A Cone To find the volume of a cone you multiply the area of the the base by the height then by one third V=1/3Bh | ## Real Life Example An ice cream cone is an example of a cone. | ## Volume Of A Pyramid To find the volume of a pyramid you multiply the area of the the base by the height then by one third V=1/3Bh |

## Volume Of A Cone

V=1/3Bh

## Example of Volume of a Cone

Answer:

V=1/3Bh

V=1/3(3.14*3^2)7

V=1/3*28.26*7

V=65.94 inches cubed.

## Example of Volume of a Pyramid

Answer:

V=1/3Bh

V=1/3(10*8)6

V=1/3*80*6

V=160 inches cubed

## All Formulas from Chapter 10

A=1/2(b1+b2)h

C=d*pi

C=2r*pi

A=pi*r^2

E=f+v-2

S=2B+Ph

S=2B+Ch

S=B+1/2Pl

S=4pi*r^2

V=Bh

V=1/3Bh

V=4/3pi*r^3

## What do the symbols mean in the formulas?

b= base

h= height

r= radius

B= area of the base

l= slant height

d= diameter

c= circumference

S= surface area

E=edges

f=faces

v= vertices

V=volume

b1= one of the parallel lines on a trapezoid

b2= one of the parallel lines on a trapezoid