SAT Mc Graw Hill 2011

The Formulas

The only area or perimeter formulas you will need for the SAT will be given at the beginning of each section:

Reference Information

r w

h

b

w

h r h c

a

b

x

2 x

x 3

s 2

s

s

A = pr^2 A = 
w

C = 2pr A = bh V =pr

(^1) V =
wh (^2) h c (^2) = a (^2) + b (^2) Special right triangles
2
45 °
45 °
60 °
30 °
The arc of a circle measures 360°.
Every straight angle measures 180°.
The sum of the measures of the angles in a triangle is 180°.
Finding the area of an obtuse triangle can
be tricky. Keep in mind that anyside can be
the base—rotate the triangle if it helps. Also
remember that an altitude mightbe outside
the triangle, as in the diagram below.
Strange Shapes
Don’t panic when you see a strange-looking
shape on an SAT. Just notice how the shape
relates to simple shapes.
Example:
In the figure below, the shaded region is con-
structed of only horizontal and vertical sides. That
is, all angles are right angles. What is the perimeter
of the shaded region?
Don’t confuse the area formula for a circle (πr^2 )
with the circumference formula (2πr). Just
remember that areas are measured in square
units, so the area formula is the one with the
radius squared.
Using Diagrams
If a geometry problem doesn’tinclude a figure,
draw one, because seeing the relationships
among the parts is essential to solving geome-
try problems! If it doesinclude a figure, mark
it up with any information you find!
You can use the diagram to estimate angle
measures and lengths, unless it is labeled “Note:
Figure not drawn to scale,” which means that
the figure is drawn inaccurately, or in only
one of many different possible ways. In this
case, it often helps to redraw the figure. If it’s
drawn inaccurately, redraw it accurately, and
see whether anything important changes. If it
can be drawn in different ways, redraw it so that
it is as different as possible from the original,
but all of the given information is maintained.

20

15

A

B

Compare the shaded region to the rectangle, but

keep in mind that the question asks about the

perimeter, not the area! Even though the areaof

the shaded region is clearly less than the areaof

the rectangle, their perimetersmust be the same!

How do we know? Consider the two different

paths from AtoB.Notice that all the horizontal

segments of the “jagged” path add up in length to

382 McGRAW-HILL’S SAT

Lesson 5: Areas and Perimeters

height

base