# Chapter 10

### Bristol M

## 10.1 Areas of Parallelograms and Trapezoids

Vocabulary:

Base of a parallelogram- the length of any of it's sides

Height of a parallelogram- perpendicular distance between the base and the opposite side

Bases of Trapezoids- are it's two parallel sides

Height of Trapezoids- perpendicular distance between the bases

## Area of a Trapezoid A=1/2(b1+b2)h Area=1/2*(base1+base2)*height | ## Real Life Example of a Trapezoid A table. Used for many different purposes. | ## Extra Practice A=1/2(b1+b2)h Write area of trapezoid=1/2(8+6)10 = 70 square centimeters |

## Area of a Parallelogram A=bh Area=base*height | ## Real Life Example of a Parallelogram Used for erasing unnecessary things. | ## Extra PracticeA=bh =10.3(6.2) Answer: 63.86 square cenimeters |

## 10.2 Areas of Circles

Area- a flat, or plane figure is the number of unit squares that can be contained within it.

Circle- the set of points that are equidistant from a special point in the plane.

Radius- half a the diameter

Circumference- computed by multiplying the diameter by pi

Pi- It expresses the ratio of the circumference to the diameter of a circle

## Area of a Circle A=pi*r^2 Area=3.14*radius to the power of 2 | ## Real Life Example of a Circle A bright, circular object that is very yummy and sweet. A orange. | ## Extra Practice A=pi*r^2 Write formula for area=3.14(8)^2 =200.96 square centimeters |

## 10.3 Three-Dimensional Firgures

Solid- three-dimensional figure that encloses a part of space

Polyhedron- a solid that is enclosed by polygons

Face- that form a polyhedron

Prism- a polyhedron, 2 congruent bases that lie in parallel planes

Pyramid- polyhedron, one base

Cylinder- solid, with 2 congruent circular bases

Cone- solid, with 1 circular base

Sphere- solid, formed by all points in space that are the same distance

Edges- segments where faces of a polyhedron meet

Vertex- a point where three or edges meet

## 10.4 Surface Areas of Prisms and Cylinders

Net- two-dimensional pattern that forms a solid when it is folded

Surface Area- of a polyhedron is the sum of the areas of it's faces

## Surface Area of a Prism S=2B+Ph Surface area=2*Area of the base+base's perimeter*height | ## Real Life Example of a Prism Dice. Used for playing any type of games. | ## Extra Practice S=2 B+Ph Write the formula of the prism=2( = 1085 square units |

## Surface Area of a Cylinder S=2B+Ch Surface area=2*area of the base+base's circumference*height S=2pir^2+2pirh Surface area=2*3.14*(radius) to the power of 2+2*3.14*(radius)*(height) | ## Real Life Example of a Cylinder A soda can. Made out of metal and very shiny. Humans drink this. | ## Extra Practice S=2pir2+2pirh Write formula for surface area=2*3.14(5)^2+2*3.14(5)(10) =471 square cenimeters |

## Surface Area of a Cylinder

Surface area=2*area of the base+base's circumference*height

S=2pir^2+2pirh

Surface area=2*3.14*(radius) to the power of 2+2*3.14*(radius)*(height)

## 10.5 Surface Areas of Pyramids and Cones

Slant height-* l* of a regular pyramid is the height of a* lateral* face, that is, any face that is not the base

## Surface Area of a Pyramid S=B+1/2Pl Surface area=area of the base+1/2*base's perimeter*slant height` | ## Real Life Example of a Pyramid Found in Egypt. Very tall and made out of very different materials. | ## Extra PracticeFind the perimeter of the base P=8+8+8=24 S=B+1/2Pl Write formula for surface area of a pyramid27.7+1/2(24)(6) =99.7 square meters |

## Surface Area of a Cone S=pir2+pirl Surface area=3.14*(radius) to the power of 2+3.14*(radius)*(slant height) | ## Real Life Example of a Cone Traffic Cone. Police use this to direct traffic. Very coneish looking shape and very bright orange. | ## Extra Practice S=pir2+pir l Write the formula for surface area of a cone
=113.04 square centimeters |

## Surface Area of a Cone

Surface area=3.14*(radius) to the power of 2+3.14*(radius)*(slant height)

## Real Life Example of a Cone

## 10.6 Volume of Prisms and Cylinders

Volume: a solid is a measure of the amount of space it occupies

measured in *cubic units*

## Volume of a Prism V=Bh Volume=area of the base*height For B= length*width | ## Real Life Example of a Prism A juice box carton. Toddlers love drinking these types of juices. | ## Extra Practice V= Bh Write formula for volume of prism= =10(5)(6) =300 cubic inches |

## Volume of a Cylinder V=Bh V=pir2h Volume=area of base*height | ## Real Life Example of a Cylinder A Spaghettios can. Very tasty. Could be eaten at lunch or maybe even at dinner. | ## Extra Practice V= Bh Write formula for volume of a cylinder= =3.14(8)^2(15) |

## Real Life Example of a Cylinder

## 10.7 Volume of Pyramids and Cones

Pyramid- polyhedron, one base

Cone- solid, with 1 circular base

Volume- a solid is a measure of the amount of space it occupies

measured in *cubic units*

## Volume of a Pyramid V=1/3Bh Volume=1/3*area of the base*height | ## Real Life Example of a Pyramid A pyramid in Egypt. Has a slanted surface. | ## Extra Practice V=1/3Bh Write formula for volume of a pyramid=1/3(30^2)(15) =4500 cubic feet |

## Volume of Cone V=1/3Bh=1/3pir^2h Volume=1/3*area of the base*height=1/3*3.14*(radius) to the power of 2*height | ## Real Life Example of a Cone Ice cream cone. Very creamy and tasty. Mostly eaten in the summertime when it is hot outside. | ## Extra Practice V=1/3 Bh Write formula for volume of a cone=1/3 =1/3*3.14(6)^2(12) =144pi =452.389 cubic feet |

## Volume of Cone

Volume=1/3*area of the base*height=1/3*3.14*(radius) to the power of 2*height

## Real Life Example of a Cone

## Volume of a Sphere V=4/3Bh Volume=4/3*area of the base*height | ## Real Life Example of a Sphere A baseball. Baseball players it is with a bat. Very round. Easy to throw. | ## Extra Practice V=4/3pir^3 Write the formula for volume of a sphere=4/3*3.14(9.6)^3 =3704.09472 cubic meters |

## Defition of Formulas

B= area of the base

C=base's circumference

V=volume

A=area

S=surface area

l=slant height

r=radius

h=height

b=base, 2-dimensional

pi=3.14

## Formulas

**10.1**

Area of a Trapezoid- A=1/2(b1+b2)h

Area of a Parallelogram- A=bh

**10.2**

Area of a circle- A=pi*r^2

**10.3**

No formulas

**10.4**

Surface Area of a Prism- S=2B+Ph

Surface Area of a Cylinder- S=2B+Ch

**10.5**

Surface Area of a Pyramid- S=B+1/2*P*l

Surface Area of a Cone- S=pi*r2+pi*r*l

**10.6**

Volume of a Prism- V=Bh

Volume of a Cylinder- V=Bh

**10.7**

Volume of a Pyramid- V=1/3*B*h

Volume of a Cone- V=1/3Bh=1/3pi*r^2*h

**Extra**

Volume of a Sphere- V=4/3*Bh

Volume of a Prism- V=__B__h-----=__lw__h

Surface Area of a Sphere- A=4*pi*r^2