Chapter 10
Sean M
10.1
Solving for trapezoids area
Perimeter=s1=s2=s3=s4
LEts do a problem
Height= 15 b1=45 b2=32
A=.5*15(45=36)
A=607.5
Parallelogram
parrallogram
parrallelagram
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
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
Examples of people using this to find area of circles
10.3
Prisms
Pyramid
cylinder
Cone
sphere
Finding the Faces Vertices and Edges
The edges is where segments of faces meet
Faces are the polygons that form 3d figures
In real life
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
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
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
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