# Chapter 10

### Mackenzie K

## Chapter 1: Area of Parallelograms and Trapezoids

## ParallelogramFormula: A=b*h Base: Is the length of any one of it sidesHeight: Perpendicular distance between the base and the opposite side. | ## Trapezoid Formula: A=1/2(b1+b2)h Base; 2 parallel sides Height: The perpendicular distance between the bases. | ## Practice Problem Your are constructing a parallelogram structure to place in the middle of town. You are given measurements to find the area of the structure. b=300ft, h=400ft. A=b*h A=300*400 (Multiply base times height) A=120,000 ft squared |

## Parallelogram

Formula: A=b*h

Base: Is the length of any one of it sidesHeight: Perpendicular distance between the base and the opposite side.

## Trapezoid

Base; 2 parallel sides

Height: The perpendicular distance between the bases.

## Area of Circle Formula A = πr^2 50 = 3.14 * r (Subtract 3.14 and add it to 50) 46.86 = r^2 (square root each number) 6.85 = r | ## Circle Circumference: The distance around the circle. Diameter: The distance across the center of the circle Radius: The distance between the center and any point on the circle. | ## Circumfrance of a Circle Formula C= πd C= 3.14 * 2 C= 6.28 |

## Area of Circle Formula

50 = 3.14 * r (Subtract 3.14 and add it to 50)

46.86 = r^2 (square root each number)

6.85 = r

## Circle

Diameter: The distance across the center of the circle

Radius: The distance between the center and any point on the circle.

## Practice Problem

A=πr^2

A= 3.14*25

A=78.5cm^2

## Chapter 3 : Three-Dimensional Figures

## Prism is a polyhedron. Have 2 congruent bases that lie in parallel planes. | ## Pyramid Is a polyhedron. Pyramids have one base. the other faces are triangles. | ## Cylinder Is a solid with 2 congruent circular bases that lie in parallel planes. |

## Cone Is a solid with one circular base. | ## Sphere Is a solid formed by all points in space that are the same distance from a fixed point called the center. | ## Practice Problem You are given a job in the mail-room and have to sort the mail. Your job is to put polyhedrons in one bin and non-polyhedrons in another. |

## Sphere

## Vocab

**Polyhedron**: is a solid that is enclosed by polygons. Only flat surfaces.

**Solid:** a 3-dimensional figure that encloses a part of space

**Faces:** The polygons that form a polyhedron

**Edges:** the segments where faces of a polyhedron meet.

**Vertex**: A point where 3 or more edges meet.

## Chapter 4: Surface Areas of Prisms and Cylinders

## Surface Area of a Prism

The Surface Area of a prism is the sum of twice the area of a base B and the product of the base's perimeter P and the height h

## Surface Area of a Cylinder

The surface area of a cylinder is the sum of twice the area of a base B and the product of the base's circumference C and the height h

## Surface Area of a Triangular Prism

S=2(1/2*b*h) + Ph

The surface area of a prism is the sum of twice the area of a base B and the product if the base's perimeter P and the height h.

## Chapter 5: Surface Areas of Pyramids and Cones

## Surface Area of a pyramid S = B + 1/2PL The surface area of a regular pyramid is the sum of the area of the base B and 1/2 the product of the base perimeter P and the slant height L. | ## Surface Area of a Cone S = πr^2 + πrL The surface area of a cone is the sum of the area of the circular base with radius r and the product of π, the radius r of the base, ad the slant height L. | ## Practice Problem You work at an ice cream truck and the boss leaves you in charge of making waffle cones. He hands you measurements and instructions on how to create waffle cones. R = 7in L= 14in S = πr^2 + πrL S = 3.14*7^2 + 3.14*7*14 S = 153.86 + 307.72 S = 461.58in^2 |

## Surface Area of a pyramid

The surface area of a regular pyramid is the sum of the area of the base B and 1/2 the product of the base perimeter P and the slant height L.

## Surface Area of a Cone

The surface area of a cone is the sum of the area of the circular base with radius r and the product of π, the radius r of the base, ad the slant height L.

## Vocab

Circumference: the distance around the circle.

Diameter: the distance across the circle through the center.

Slant Height: the height of any face that is not the base of a regular pyramid

## Chapter 6: Volumes of prisms and Cylinders

## Volume of a Prism V = Bh The volume of a prism is the product of the area of the base B and the height h | ## Volume of a Cylinder (V = Bh) V = πr^2h The volume of a cylinder is the product of the area of a base B and the h. | ## Practice Problem Your teacher has given you two crates and you have to figure out the volume of the triangular and circular crate. Triangular: V=Bh Circular: V=πr^2h V=1/2*4*5*8 V=3.14*5^2*5 V=80in^3 V=392.5in^3 |

## Volume of a Prism

The volume of a prism is the product of the area of the base B and the height h

## Volume of a Cylinder

V = πr^2h

The volume of a cylinder is the product of the area of a base B and the h.

## Chapter 7: Volumes of Pyramids and Cones

## Volume of a Pyramid V= 1/3Bh The volume V of a pyramid is 1/3 the product of the area of the base B and the height h. | ## Volume of a Cone V= 1/3Bh= 1/3πr^2h The volume of a cone V is 1/3 the product of the area of the base B and the height h. Related to Cylinders | ## Practice Problem To figure out the volume of a cone you must....... Find the formula and input numbers for letters. V= 1/3πr^2h V=1/3^3.14*3^2*6 V=56.52ft^3 |

## Volume of a Pyramid

The volume V of a pyramid is 1/3 the product of the area of the base B and the height h.

## Volume of a Cone

The volume of a cone V is 1/3 the product of the area of the base B and the height h.

Related to Cylinders

## Formulas

Chapter 1

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

- Area of a Circle: A=πr^2

- Surface Area of a Prism: S=2B+Ph
- Surface Area of Cylinder: 2πr^2 + 2πrh

- Surface Area of Pyramid: S= B+1/2PL
- Surface Area of a Cone: S= πr^2 + πrL

- Volume of a Prism: V=Bh
- Volume of a Cylinder: V=πr^2h

- Volumes of a Pyramids: V=1/3Bh
- Volumes of a Cone: V=1/3πr^2h

- Area of a triangle: A= bh1/2