# Chapter 10

### Sean M

## 10.1

## Parallelogram Here is a trapezoid. On one of the heights like AE imagine that you cut along the height. You now have a triangle but you then can go attach this to the other side of the parallelogram and there you have a rectangle. | ## parrallogram Here show where you cut the triangle off | ## parrallelagram then you can simply put the triangle you cut off on the other side of the trapezoid to make a rectangle. Then you may multiply the base length by the height of the Rectangle to get the area[top eraser a great example of a Parallelogram!] |

## Parallelogram

## How to solve a problem like this

Example:

Base:15mm Height:10mm

Formula= A=b*h

Solve A=15*10

A=150mm2<-REMEMBER TO SQUARE THE AREA

## 10.2

## Finding the Areas of Circles

**π**is multiplied by the radius squared or 2. A=3.14*r2

Lets solve one.

So your Radius is 10ft and use 3.14 for pi

A=3.14*r2

A=3.14*10 2

A=3.14*100

A=314ft2< Remember to square the answer

## 10.3

## Prisms Have to congruent which means they are the same bases. the other sides are rectangles | ## Pyramid is a polyhedron, have only one base other sides are triangles | ## cylinder solid with 2 congruent circular bases that lie parallel planes |

## 10.5

## The formula and how to solve for a pyrimid

B is the base of the pyramid which means you must use the formula for that shape

P is the length of one of the sides in the base

l= length or called slant height from the side of the base to the top vertex

Example: Base Rectangle 15in by 12in l= 34in P=12in

SA=15*12+.5*12*34

SA=384in.2

## Finding the surface area of a Cone

**π**r2 +

**πrl**

r=radius

L=slant height

Lets do one

Radius= 5 feet Height= 12 feet

With this problem you need to use the pythagorean theorem to find the slant height.

Which is A2+B2=C2

So 5*5+12*12=c2

169=c2 But now you must square root 169

C=13 feet

Finally

SA=pi*r2+pi*r*l

SA=pi*5^2+pi*5*13

SA=282.2 Feet^2 Remember to square your answer

## Finding the volume of a cylinder

V=Bh

B=3.14*r2

Example:

Radius= 6cm Height= 3cm

so the area of the circle you do

Area=3.14*6^2 = 113.04 then..

113.04*3= 339.12cm3 **REMEMBER TO CUBE THE ANSWERS AND ADD A LABEL!**

## 10.7

Formula for a Pyramid: **V=1/3Bh**

B=Base

h=Height

Lets do one

length1 15in length2= 15in slant height=16in

so first you want to divide the length 1 by 2 to get 7.5 this is one base of a triangle You then use the pythagorean theorem to get the length from the middle to the top vertex this is... 17.7in you then plug in the formula for the base A=bh= 225in^2 then multiply by 1/3 and then multiply by 17.7 to get you answer of 1327.5in^3

## Volume of a Cone

The base is the area of a circle pi*r2

Then you use the height of the center of the circle to the top of the cone

## Formulas

Area of a Trapezoid=A=.5(b1=b2)h

Area of a Circle=3.14*r2

Surface area of a Prism=SA=2b=Ph or just find the area of all the shapes and add

Surface area of a Cylinder=SA=2B=Ch or just do the same as in the Prism ex.

Surface area of a Pyramid=SA=B=.5Pl

Surface area of a Cone=SA=3.148r2=3.14*r*l

Volume of a Prism=V=Bh

Volume of a Cylinder=Bh but with a circle base

Volume of a Pyramid=V=1/3Bh

Volume of a Cone=V=1/3Bh no slant height

Volume of a Sphere=V=4/3*3.14r3

Surface area of a Sphere= SA=3.14*4*r2