Chapter 7
SIMPLIFY:
20 12 3
20 = 4 5 = 2 5
12 3 12 3 3 3 3
4 3= =
MULTIPLY:
( 2 5 )2
(2 5 )2 = 4 25 = 4 5 = 20.
COMPLETE:
( ___ )2 + ( ___ )2 = ( ___ )2
leg1
leg2
hyp
(leg1)2 + (leg2)2 = (hyp)2
Pythagorean Theorem
Complete to form RIGHT triangles:
3, 4, ____ 5, 12, ____
6, 8, ____ 8, 15, ____
3, 4, 5 5, 12, 13 6, 8, 10 8, 15, 17
Given segment lengths a, b, c longest
Right c2 a2 + b2
Obtuse c2 a2 + b2
Acute c2 a2 + b2
Right c2 = a2 + b2
Obtuse c2 > a2 + b2
Acute c2 < a2 + b2
COMPLETE:
L = ____
H = ____
45
45
L = L
H = L 2
SOLVE:
x = _____
y = _____
8
x
y45
45
x = 8
y = 8 2
COMPLETE:
LL = _____
H = _____30
60
Ls
LL = Ls 3
H = 2 Ls
SOLVE:
x = _____
y = _____30
604
x
y
x = 4 3
y = 8
AREA OF EQUILATERAL TRIANGLES:
A = ½ ( ____ )( ____ )
A = ½ ( ____)( ____ )
A = ( ____ )2
( ____ )
A = ½ bh
A = ½ ap
A = s2 4
3
Find the area:
(Equilateral Triangle)
6 3
30
63
9
18
33
A = ½ bh
A = ½ (18)(9 )
A = 81
3
3
A = ½ ap
A = ½ (3 )(54)
A = 81
3
3
A = s2 4
A = (18)2
4
A = 81
3
3
3
AREA OF SQUARES:
A = ( ____ )2
A = ½ ( ____ )( ____ )
A = ½ ( ____ )( ____ )
A = s2 A = ½ ap A = ½ d1d2
side (s)
a
Find the area:
(Square)
10 2
10 210
10
20
A = s2
A = 202
A = 400
A = ½ ap
A = ½ (10)(80)
A = 400
A = ½ d1d2
A = ½ (20 )(20 )
A = 400
2 2
45
AREA OF REGULAR HEXAGONS:
A = ½ ( ____ )( ____ )
A = ½ ap
120
a60
Find the area:
8
(Regular Hexagon)
8
4 4
4 3
60
A = ½ ap
A = ½ (4 3)(48)
A = 96 3
AREA OF PARALLELOGRAMS:
A = ( ____ )( ____ )
A = bh
Base (b)
Height (h)
AREA OF ANY TRIANGLE:
A = ½ ( ____ )( ____ )
A = ½bh
base (b)
height (h)
Find the height:
6 6
4
h2 + 22 = 62
h2 = 32h = 32 = 4 2
6 6
4
2 2
h
AREA OF RIGHT TRIANGLES:
A = ½ ( ____ )( ____ )
A = ½ (l1)( l2)
leg (l1) leg (l2)
AREA OF RHOMBUSES:
A = ½ ( ____ ) ( ____ )
A = ½ (d1)(d2)
AREA OF TRAPEZOIDS:
A = ½ ( ____ ) ( ____ + ____ )
A = ½ (h)(b1 + b2)
base (b1)
base (b2)
height (h)
FOR CIRCLES:
Circumference = ( __ )( __ )( __ )
C = 2rπ
What fraction of the circumference is arc AB?
r
120o
A
B
120 = 1 360 3
AREA OF CIRCLES:
A = ( ____ )( ____ )2
A = πr2
What fraction of the circle is shaded?
450
r
45 = 1 360 8