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Chapter12

VIEWS: 6 PAGES: 4

									Areas and perimeters

r: the radius θ: the interior angle s: the length of the arc

The area of the circle:
A    r2

In general, if you find the radius of the circle, then you will be able to answer any question regarding circles in the SAT. There is also a very interesting and useful proportion that can be used to calculate the area of the circle:
A AT  s 360º 

where AT is the total area, As is the area of the sector and θ is the measure in degrees of the interior angle. If you have the interior angle you can calculate the amount of equal sectors inside the circle by dividing 360 by the measure of the interior angle:
# Sectors  360º



The area of each sector is:
As  AT # Sectors

The circumference of a circle is the length around it. The circumference of a circle can be calculated from its diameter using the formula:

Or, substituting the radius for the diameter:

With the information above you can solve any problem regarding circles.

Squares and rectangles d L W The area of a rectangle or a square is: A=L x W The perimeter is: P= 2L + 2W The diagonal can be obtained, if needed, using the Pythagoras Theorem which was explained in Chapter 11. The trapezoid b d h b: small base B: large base h: height d: diagonal L: lengh W: width d: diagonal

B

A

B  b   h
2

P  2d  B  b

The diagonal can be obtained, if needed, using the Pythagoras Theorem which was explained in Chapter 11. The sum of the interior angles of any figure with 4 sides is 360º.

Volumes In parallelograms the volume is obtained multiplying the length times the width times the height as follows:
V  L W  H

If the figure is a cube then:

V  L L L

In the case of the cylinder the area equals the area of the base times the height.

V    r2  h

There might also be problems where you will be asked to find the number of squares that fit in a bigger square (2-D) or the number of small parallelograms that fit in a larger parallelogram (3-D). In this scenario use the following formulas: 2-D

# items 

total area of larger figure individual area of small figure

Example: How many square bathroom tiles with side = 4 cm can fit in a wall with dimensions 24cm by 18 cm? Solution: Just apply the formula. The individual area of each tile is 16 cm 2. The total area is 432 cm2. Substituting in the formula we get:
# items  432 16

#items = 27 3-D

# items 

total volume of larger figure individual volume of small figure

Example: How many cylinders with radius 4 cm and height 20 can fit in a cylinder with a volume of 26880π cm3. Solution: Just apply the formula for volumes. The individual volume of each cylinder is 320π cm3. Substituting in the formula we get:
# items  26880 320

#items = 84


								
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