Geometry Formulas Flashcards

Area Formulas

• Area of a Triangle: ( a = \frac{1}{2}bh )
• Area of a Rectangle: ( a = bh )
• Area of a Circle: ( a = \pi r^2 )
• Area of a Parallelogram: ( A = bh )
• Area of a Trapezoid: ( A = \frac{(b_1 + b_2)h}{2} ) or ( A = \frac{1}{2}(b_1 + b_2)h )
• Area of a Rhombus: ( A = \frac{1}{2}d_1d_2 )
• Area of a Kite: ( A = \frac{1}{2}d_1d_2 )
• Area of a Regular Polygon: ( A = \frac{1}{2}aP ) (where ( a ) is the apothem and ( P ) is the perimeter)

Perimeter and Circumference

• Perimeter of a Rectangle: ( p = 2(l + w) )
• Perimeter of a Triangle: ( p = \text{side 1} + \text{side 2} + \text{side 3} )
• Circumference of a Circle: ( c = 2\pi r ) or ( c = \pi d )

Volume Formulas

• Volume of a Prism: ( V = B \times h ) (where ( B ) is the area of the base)
• Volume of a Cylinder: ( V = B \times h ) (with ( B = \pi r^2 ))
• Volume of a Pyramid: ( V = \frac{1}{3}B \times h )
• Volume of a Cone: ( V = \frac{1}{3}B \times h ) (with ( B = \pi r^2 ))
• Volume of a Sphere: ( V = \frac{4}{3} \pi r^3 )

Surface Area Formulas

• Surface Area of a Prism: ( SA = 2B + (\text{perimeter} \times \text{height}) )
• Surface Area of a Cylinder: ( SA = 2B + (\text{circumference} \times \text{height}) )
• Surface Area of a Pyramid: ( SA = B + \frac{1}{2}(\text{perimeter} \times \text{slant height}) )
• Surface Area of a Cone: ( SA = B + \frac{1}{2}(\text{circumference} \times \text{slant height}) )
• Surface Area of a Sphere: ( SA = 4\pi r^2 )

Triangle and Polygon Classification

• Triangle: A 3-sided polygon
• Quadrilateral: A 4-sided polygon
• Pentagon: A 5-sided polygon
• Hexagon: A 6-sided polygon
• Heptagon: A 7-sided polygon
• Octagon: An 8-sided polygon
• Nonagon: A 9-sided polygon
• Decagon: A 10-sided polygon
• Dodecagon: A 12-sided polygon
• n-gon: An n-sided polygon

Trigonometric Functions

• Sine (SOH): ( \frac{\text{Opposite}}{\text{Hypotenuse}} )
• Cosine (CAH): ( \frac{\text{Adjacent}}{\text{Hypotenuse}} )
• Tangent (TOA): ( \frac{\text{Opposite}}{\text{Adjacent}} )
• Inverse Sine: ( \sin^{-1} )
• Inverse Cosine: ( \cos^{-1} )
• Inverse Tangent: ( \tan^{-1} )

Important Theorems and Formulas

• Pythagorean Theorem: ( a^2 + b^2 = c^2 )
• Distance Formula: ( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} )
• Slope Formula: ( m = \frac{(y_2 - y_1)}{(x_2 - x_1)} )
• Midpoint Formula: ( M = \left[\frac{(x_1 + x_2)}{2}, \frac{(y_1 + y_2)}{2}\right] )

Line Equations

• Point-Slope Form of a Line: ( (y - y_1) = m(x - x_1) )
• Slope-Intercept Form of a Line: ( y = mx + b )
• Equation of a Vertical Line: ( x = x_1 )
• Equation of a Horizontal Line: ( y = b )

Laws of Trigonometry

• Law of Sines: ( \frac{\sin(A)}{a} = \frac{\sin(B)}{b} = \frac{\sin(C)}{c} )
• Law of Cosines: ( a^2 = b^2 + c^2 - 2bc \cos(A) )

Reciprocal Relationships

• If slope of a line is ( \frac{a}{b} ), the slope of the perpendicular line is ( \frac{-b}{a} )