Chapter 10

Sean M

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

10.2

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.

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

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

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

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:

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

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