# Chapter 10

### Jamie W.

## Section 10.1

__Area of a Parallelogram__

- Formula: A=b x h
- Base multiplied by height

__Area of a Trapezoid__

- Formula: A=1/2(b1+b2)h
- Base 1 and Base 2 are the two bases, doesn't matter which is which
- Add base 1 and base 2 together, then multiply by the height, then multiply by 1/2
- Height on a slant, perpendicular to the base

__Area of Squares__

- Formula: A=b x h
- Base times height
- Same as parallelogram

__Area of a Triangle__

- Formula: 1/2 x b x h
- Half times base times height
- Square/Parallelogram divided by 2

## Section 10.2

__Area of a Circle__- Formula: pi x radius squared
- pi= 3.14, 22/7, or pi button

The following video explains how to get the area of a circle clearly. It also shows that if you only have the diameter of the circle, you can still figure out the area by dividing the length of the diameter by 2 to get the radius.

## Section 10.3

__Solids Classification__**Prisms: **

- have two congruent bases (same size, same shape)
- other faces are rectangles
- named by the shape of it's base (i.e: rectangular prism)

**Pyramids:**

- has one base, that is a certain shape like a prism

- named for shape of it's base (i.e: triangular pyramid)
- other faces are triangles
- faces come to a vertex at the top

**Cylinder:**

- has two congruent bases
- bases always circular
- bases always parallel
- no faces, edges, or vertices

## Prism This is an example of a prism. (rectangular) | ## Pyramid This is an example of a pyramid. (triangular) | ## Cylinder This is an example of a cylinder. As you can see, it always has circular bases, as stated above. |

## More Solids

Cone:

- has one circular base
- no faces or edges
- lateral surface comes to point at top
- similar to pyramid, only circular and no triangular faces

Sphere:

- basically a ball
- formed by all points in space that are the same distance from a fixed point called the center

## Cone

## Section 10.4

## Surface Area of a Prism

s=2B+Ph

Area of the base multiplied by 2,

plus the perimeter times the height

## Surface Area of a Cylinder

s=2B+Ch=2*pi*r^2+2*pi*r*h

Area of the base multipied by 2,

plus the circumference times the height

Circumference: 2*pi*radius

The following video clearly teaches you about the surface area of prisms and cylinders.

## Section 10.5

## Surface Area of a Pyramid

B+1/2Pl

Area of the base,

plus one half the product

of the perimeter and the slant height.

## surface area of a cone

pi*r^2+pi*r*l

Area of the base (pi*r^2)

plus the product of pi times

the radius times the slant height

## Section 10.6

**is the amount of space that an object occupies.**

__Volume__## Volume of a prism

Bh

area of the base

times the height.

## volume of a cylinder

Bh

area of the base (pi*r^2)

times the height

## Section 10.7

## volume of a pyramid

1/3Bh

area of the base multiplied

by the height, times one third.

## Volume of a cone

1/3*Bh=1/3*pi*r^2*h

area of the base times the height,

multiplied by one third.

area of the base: pi*radius^2

## Real Life Tie-Ins

Some of the most modern examples are:

- The Equator and Prime Meridian (perpendicular lines)
- Hershey's Kiss (cone)
- Pyramids of Egypt (pyramid)