Geometry Formulas Flashcards

Flashcards covering geometry formulas for an upcoming test.

Area of a Square

A = s²

Area of a Rectangle

A = lw

Area of a Triangle

A = ½bh

Area of a Circle

A = πr²

Area of a Parallelogram

A = bh

Area of a Trapezoid

A = ½(b₁ + b₂)h

Circumference of a Circle

C = 2πr

Pythagorean Theorem

c² = a² + b²

Equation of a Line

y = mx + b

Equation of a Circle

(x − h)² + (y - k)² = r²

Sine (sin θ)

opposite / hypotenuse

Cosine (cos θ)

adjacent / hypotenuse

Tangent (tan θ)

opposite / adjacent

Cosecant (csc θ)

hypotenuse / opposite

Secant (sec θ)

hypotenuse / adjacent

Cotangent (cot θ)

adjacent / opposite

Volume of a Rectangular Prism

V = lwh

Volume of a Cube

V = s³

Volume of a Cylinder

V = πr²h

Area of a Square

A = s²
Example: Find the area of a square with side length 5. A = 5^2 = 25

Area of a Rectangle

A = lw
Example: Find the area of a rectangle with length 8 and width 4. A = 8 * 4 = 32

Area of a Triangle

A = ½bh
Example: Find the area of a triangle with base 6 and height 7. A = (1/2) * 6 * 7 = 21

Area of a Circle

A = πr²
Example: Find the area of a circle with radius 3. A = π * 3^2 ≈ 28.27

Area of a Parallelogram

A = bh
Example: Find the area of a parallelogram with base 10 and height 5. A = 10 * 5 = 50

Area of a Trapezoid

A = ½(b₁ + b₂)h
Example: Find the area of a trapezoid with bases 4 and 6, and height 3. A = (1/2) * (4 + 6) * 3 = 15

Circumference of a Circle

C = 2πr
Example: Find the circumference of a circle with radius 4. C = 2 * π * 4 ≈ 25.13

Pythagorean Theorem

c² = a² + b²
Example: Find the hypotenuse of a right triangle with sides a = 3 and b = 4. c^2 = 3^2 + 4^2 , c = \sqrt{25} = 5

Equation of a Line

y = mx + b
Example: Find the equation of a line with slope 2 and y-intercept 1. y = 2x + 1

Equation of a Circle

(x − h)² + (y - k)² = r²
Example: Find the equation of a circle with center (2, 3) and radius 5. (x - 2)^2 + (y - 3)^2 = 25

Sine (sin θ)

opposite / hypotenuse
Example: In a right triangle, if the opposite side is 3 and the hypotenuse is 5, then sin θ = 3/5 = 0.6

Cosine (cos θ)

adjacent / hypotenuse
Example: In a right triangle, if the adjacent side is 4 and the hypotenuse is 5, then cos θ = 4/5 = 0.8

Tangent (tan θ)

opposite / adjacent
Example: In a right triangle, if the opposite side is 3 and the adjacent side is 4, then tan θ = 3/4 = 0.75

Cosecant (csc θ)

hypotenuse / opposite
Example: If sin θ = 0.6, then csc θ = 1/0.6 ≈ 1.67

Secant (sec θ)

hypotenuse / adjacent
Example: If cos θ = 0.8, then sec θ = 1/0.8 = 1.25

Cotangent (cot θ)

adjacent / opposite
Example: If tan θ = 0.75, then cot θ = 1/0.75 ≈ 1.33

Volume of a Rectangular Prism

V = lwh
Example: Find the volume of a rectangular prism with length 6, width 4, and height 5. V = 6 * 4 * 5 = 120

Volume of a Cube

V = s³
Example: Find the volume of a cube with side length 4. V = 4^3 = 64

V = πr²h
Example: Find the volume of a cylinder with radius 2 and height 7. $$V = π * 2^2 *