Download Chapter 8 Area Formulas

Chapter 7 Formulas
Hint: Simplify all ratios/fractions – make sure they have the same units!
Ways to prove Triangles are Similar (same angles, sides are proportional)
AA~, SAS~, SSS~
Midsegment = half of the base
Ratio of sides is the SAME as ratio of perimeters
How to find scale factor: find two sides that are corresponding and put one value over the other,
then simplify!
Chapter 8 Area Formulas
Sum of the interior angles of a polygon: (𝒏 − 𝟐) ∙ 𝟏𝟖𝟎°
Area of a Rectangle: 𝑏ℎ
Area of a Square:
Area of a parallelogram: 𝑏ℎ
Area of a rhombus:
Sum of the exterior angles: 360 °
𝑑 1 𝑑2
2
Arc length=
Area of a circle: 𝜋𝑟 2
Area of a sector =
a∙p
2
Area of a Trapezoid:
𝒎𝒆𝒂𝒔𝒖𝒓𝒆 𝒐𝒇 𝒄𝒆𝒏𝒕𝒓𝒂𝒍 𝒂𝒏𝒈𝒍𝒆
∙
𝟑𝟔𝟎
Circumference of a circle: 2πr or πd
Area of a regular polygon:
Area of a Triangle:
𝑠2
2πr
𝒎𝒆𝒂𝒔𝒖𝒓𝒆 𝒐𝒇 𝒄𝒆𝒏𝒕𝒓𝒂𝒍 𝒂𝒏𝒈𝒍𝒆
∙
𝟑𝟔𝟎
𝜋𝑟 2
Perimeter: 𝑛 ∙ 𝑠
Chapter 9 Surface Area & Volume Formulas
B = AREA of the base
SURFACE AREA FORMULAS
P = PERIMETER of the base
VOLUME FORMULAS
Prism: 2B + Ph
Prism: Bh
Cylinder: 2𝜋𝑟 2 + 2𝜋𝑟ℎ
Cylinder: 𝜋𝑟 2 ℎ
1
1
Pyramid: B + 2 𝑃𝑙
Pyramid: 3 𝐵ℎ
Cone: 𝜋𝑟 2 + 𝜋𝑟𝑙
Cone: 𝜋𝑟 2 ℎ
Sphere: 4𝜋𝑟 2
Sphere: 3 𝜋𝑟 3
1
3
4
𝑏ℎ
2
ℎ(𝑏1 +𝑏2 )
2
Chapter 10 Formulas
BELOW ARE THE PERFECT SQUARES
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225
Pythagorean Theorem: 𝑎2 + 𝑏 2 = 𝑐 2 Use for finding sides of right triangles
45˚-45˚-90˚ triangle:
HYPOTENUSE = leg • √2
𝑥√ 2
30˚- 60˚ - 90˚ triangles
Hypotenuse = 2 • short leg
Long leg = short leg • √3
TRIGONOMETRY for RIGHT Triangles!
SOH
CAH
𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆
𝐬𝐢𝐧 𝜽 = 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆
𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕
𝐜𝐨𝐬 𝜽 = 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆
TOA
𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆
𝐭𝐚𝐧 𝜽 = 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕
Use the inverse functions to find ANGLES
𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆
Θ = sin-1(𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆)
𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕
Θ = cos-1(𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆)
𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆
Θ = tan-1(𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕)
CHAPTER 11 Formulas
A
x°
Pythagorean
Theorem
𝑎2 + 𝑏 2 = 𝑐 2
r
Semicircle=180
If hyp is the diameter
Then angle = 90
Opposite angles
add up to 180
ANGLE RELATIONSHIPS
Angle ON Circle
Central Angle
1
angle = arc
Arc Length Formula
x°
B arc length of AB = 360° • 2πr
1
angle = arc
angle = arc
2
2
Angle INSIDE Circle
1
angle = (arc + arc)
2
Angle OUTSIDE Circle
1
angle = 2 (large arc – small arc)
SEGMENT RELATIONSHIPS
a∙b=c∙d
b(a + b) = d(c + d)
a2 = c(b + c)