# Chapter 10

## 10.1

In this section you are taught how to find the areas of Parallelograms and trapezoids. To find the area of these you must consider a rectangle. Both parallelograms and trapezoids are rectangles without right angles. If you along the angle (shown in picture)

## Solving for trapezoids area

Formula= A=1/2h*(b1=b2)

Perimeter=s1=s2=s3=s4

LEts do a problem

Height= 15 b1=45 b2=32

A=.5*15(45=36)

A=607.5

## How to solve a problem like this

First look at the height and the base and "plug them into the equation/formula"

Example:

Base:15mm Height:10mm

Formula= A=b*h

Solve A=15*10

A=150mm2<-REMEMBER TO SQUARE THE AREA

## Finding the Areas of Circles

In this section we learn to solve the area of circles. To do this you need the formula of A=3.14orπis multiplied by the radius squared or 2. A=3.14*r2

Lets solve one.

A=3.14*r2

A=3.14*10 2

A=3.14*100

A=314ft2< Remember to square the answer

Area of a Circle - MathHelp.com - Math Help

## Examples of people using this to find area of circles

Some people need to use this formula to do a job like a architect designing a silo. The must find the exact size of the silo to tell the builder how large to make and not order to many materials.

## 10.3

Classifying 3d objects

## Finding the Faces Vertices and Edges

The vertex is where 3 or more points meet

The edges is where segments of faces meet

Faces are the polygons that form 3d figures

## In real life

You may need this formula to find the amount of siding you need for your house

## 10.5

Finding the surface area of pyramids and cones

## The formula and how to solve for a pyrimid

Formula: S=B+.5*Pl

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

The formula SA= πr2 +πrl

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

## 10.6

Finding the volume of Prisms and Cylinders

Formula= V=Bh

B=base which depends on the shape of it

h= height of the 3d object

Example length=5m length2=3m length3= 4m

So..

To find base you multiply length1 with 3

4m*5m=20m2

20 then is * by 3 to get the volume which it 60m3 the 3 is the cubed symbol

## Finding the volume of a cylinder

Formula= the same as the prism by you have a circle for a base

V=Bh

B=3.14*r2

Example:

so the area of the circle you do

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

## 10.7

Finding the volume of Pyramids,Cones and spheres

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

Formula=V=1/3 * Bh

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

Volume of a Pyramid - MathHelp.com - Math Help

## Formulas

Area of a Parallelogram=A=bh

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