# Chapter 10

### Rachel Botic Hr. 7

## 10.1- areas of parallelograms and trapezoids

__Vocabulary:__

***Base of a Parallelogram:** is the length of any one of it's sides

***Height of a Parallelogram:** the perpendicular distance between the base and the opposite side

***Bases of a Trapezoid:** are it's two parallel sides

***Height of a Trapezoid:** the perpendicular distance between the bases

## 10.2- Areas of Circles

__Vocabulary:__

***Area:** the amount of surface the figure covers

***Circle:** is the set of all points in a plane that are the same distance from a fixed point in the center

***Radius:** the distance from the center to any point on the circle

***Diameter:** is the distance across the circle that crosses through the center of the circle

***Circumference:** the distance around the circle

***Pi:** the non-repeating decimal that we use for finding the circumference and area of a circle

## video on how to find the circumference of a circle

## real life example for circumference

## 10.3 three-dimensional figures

__Vocabulary:__***solid:** a three dimensional figure that encloses a part of space

***polyhedron:** a solid that is enclosed by polygons

***face:** the polygons that form a polyhedron

***prism:** is a polyhedron, that has two congruent bases that are parallel to each other.

***pyramid:** is a polyhedron, that has one base, and the other faces are triangles

***cylinder:** is NOT a polyhedron, and is a solid with two bases that are parallel to each other.

***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.

***edge:** the segments where faces of a polyhedron meet

***vertex:** is a point where three or more edges meet.

## Example of a Prism A prism can be a tissue box for a real life example. | ## Example of a Pyramid A pyramid is like one of the Ancient Egyptian Pyramids that are in Egypt, for a real life example. | ## Example of a Cylinder A cylinder is like a soup can it has two bases which are circles, and aren't polyhedrons. |

## Example of a Pyramid

## Example of a Cone A cone can be a waffle ice cream cone for a real life example of a cone. | ## example of a sphere A sphere can be a volleyball for an example in real life |

## 10.4 surface areas of prisms and cylinders

__Vocabulary:__

***net:** a two-dimensional pattern that forms a solid when it is folded

***surface area:** is the sum of the area of it's faces.

## how to find the surface area of a prism

S=2B+Ph-----------------------------------Write out formula first

S=2(1/2x10x12)+(13+13+10)15----Then fill in the numbers to solve

S=660** units2**----------------------------Multiply

****Labels!!** **

****For a triangular prism remember to multiply by 1/2!****

## How to find the surface area of a cylinder

S=2TTr2+2TTrh--------------Write out formula first

S=2TT(4)2+2TT(4)(10.7)---Fill in numbers to solve

S=369.45 **units2**------------Multiply

****Labels!!****

## 10.5 surface areas of pyramids and cones

**Vocabulary:**

***slant height:** or l of a regular pyramid is the height of a lateral face, which is, any face that isn't the base

## video on how to find the surface area of a pyramid

## 10.6 Volumes of Prisms and cylinders

__Vocabulary:__

***volume:** is a measure of a solid's amount of space it takes up

## 10.7 volumes of pyramids and cones

__Vocabulary:__

***pyramid:** is a polyhedron, that has one base as any polyhedron, with the other faces as triangles

***cones:** a solid with one circular base

***volume:** is a measure of a solid and how much space it takes up

## video on how to find the volume of a pyramid

## All formulas in chapter 10

## 10.1 formulas

Area of a Parallelogram: A=bh

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

## 10.2 formulas

Area of a Circle: A=TTr2

Circumference: C=TTd or C=2TTr

## 10.4 formulas

Surface Area of a Prism: S=2B+Ph Triangular: S=1/2(2)B+Ph

Surface Area of a Cylinder: S=2B+Ch **OR **S=2TTr2+ 2TTrh

## 10.5 formulas

Surface Area of a Pyramid: S=B+1/2Pl "B"=area of the base-lw

Surface Area of a Cone: S=TTr2+TTrl

## 10.6 formulas

Volume of a Rectangular Prism: V=Bh "B"=area of the base-lw

Volume of a Triangular Prism: V=Bh "B"=area of the base-1/2lw

Volume of a Cylinder: V=Bh "B"=area of the base-TTr2

## 10.7 formulas

Volume of a Pyramid: V=1/3Bh "B"=area of the base-lw

Volume of a Cone: V=1/3Bh "B"=area of the base-TTr2

Volume of a Sphere: V=4/3TTr3

Surface Area of a Sphere: A=4TTr2