Aim: How do we find surface area and lateral area of prisms and cylinders?

Prisms is a solid with bases that are 2 congruent polygons. The other sides of the prisms are called the lateral faces.

Surface Area : Lateral area + area of the two ends(bases)
Lateral area: Perimeter of the base*height
Surface area : perimeter of base* height + 2(Area of the base)

Cylinders


Surface Area: Areas of top and bottom +Area of the side
Lateral area: 2*pi*r*h
Surface area: Surface Area = 2(pi r ²) + (2 pi r)* h

http://www.mathsteacher.com.au/year7/ch09_polygons/06_polyhedra/Image11220.gif
http://cf.ydcdn.net/1.0.0.30/images/main/A4cylind.jpg

WHAT IS THE SURFACE AREA OF A SPHERE?

how do we do compositions of transformations?

• Compositions of transformations are when 2 or more transformations are combined to form a new transformation.
• In a composition, you do the second one FIRST.

          SOMETIMES Written and ALWAYS rule:



EXAMPLE:

 

 

Sources:

http://www.regentsprep.org/Regents/math/geometry/GT6/composition.htm

how do we do the compositions of 3 transformations?

How do we define circles?

What is a circle?

• the set of all points in a plane at a given distance from a given point
• Given distance is called a RADIUS
• Given point is called a CENTER

Chord

• A line segment that connects two points on a circle



Diameter

• A line segment through the center of a circle with endpoints on the circle.
• Longest chord in the circle

Tangent

• A line that touches a circle in exactly one point.
• Two circles can be tangent at the same line and same point.

Arc

• An arc is a portion of the circumference of a circle.

Resources:

• http://www.mathatube.com/images/circle-lines_1_.gif

Any other lines or segments in a circle?

How do we calculate distance?

To calculate distance from two endpoints, you use the formula:

Distance Formula:


Example: Find distance between the two points : (-1,-2) and (9,-10)
1st step :use the distance formula

2nd step : square root* of (-1-9)^2+ (-2-(-10))^2
3rd step: square root of (-10)^2+(8)^2
4th step: square root of 100+64
5th step: square root of 164
6th step: 2 square root of 41
*square root:

Resources:
http://0.tqn.com/d/math/1/0/A/1/distance.gif
http://www.moomoomath.com/distance.jpg

Can you use this distance formula to calculate distances in shapes?