Geometry Formula Sheet Review

A set of question-and-answer flashcards covering essential circle theorems, right-triangle relations, coordinate-geometry formulas, and area, perimeter, surface-area, and volume formulas for common plane and solid figures.

What is the sum of the interior angles of an n-sided polygon?

180°(n − 2)

How do you calculate the circumference of a circle with radius r?

C = 2πr

How do you calculate the area of a circle with radius r?

A = πr²

What is the perimeter of a rectangle with length l and width w?

P = 2l + 2w

What is the area of a rectangle with length l and width w?

A = lw

What is the perimeter of a square with side s?

P = 4s

What is the area of a square with side s?

A = s²

How do you find the area of a triangle with base b and height h?

A = ½bh

What are the perimeter and area formulas for a parallelogram with base b, side a, and height h?

P = 2a + 2b  A = bh

How do you find the area of a trapezoid with bases a and b and height h?

A = ½h(a + b)

What is Euler’s formula that relates vertices, edges, and faces of a polyhedron?

V − E + F = 2

What is the surface area of a right circular cylinder?

SA = 2πr² + 2πrh

What is the volume of a right circular cylinder?

V = πr²h

What is the surface area of a rectangular prism with length l, width w, and height h?

SA = 2lw + 2lh + 2wh

What is the volume of a rectangular prism?

V = lwh

What is the surface area of a sphere with radius r?

SA = 4πr²

What is the volume of a sphere with radius r?

V = (4⁄3)πr³

What is the surface area of a right circular cone with radius r and height h?

SA = πr² + πr√(r² + h²)

What is the volume of a right circular cone?

V = (1⁄3)πr²h

What is the general volume formula for any pyramid with base area B and height h?

V = (1⁄3)Bh

How do you find the measure of an angle formed by two chords intersecting inside a circle?

x = ½(m + n) where m and n are the intercepted arcs

How do you find the measure of an angle formed by a tangent and a chord?

x = ½n where n is the intercepted arc

How do you find the measure of an angle formed outside a circle by two secants, a secant and a tangent, or two tangents?

x = ½(m − n) where m is the larger intercepted arc and n is the smaller

What is the product of the segments of two intersecting chords inside a circle?

a·b = c·d

What is the power-of-a-point formula for a tangent and a secant drawn from the same external point?

a² = b(b + c)

What is the power-of-a-point formula for two secants drawn from the same external point?

b(a + b) = d(c + d)

What relationship exists between two tangents drawn from the same external point to a circle?

Their lengths are equal (a = b).

What is the definition of sin θ in a right triangle?

sin θ = opposite ⁄ hypotenuse

What is the definition of cos θ in a right triangle?

cos θ = adjacent ⁄ hypotenuse

What is the definition of tan θ in a right triangle?

tan θ = opposite ⁄ adjacent

State the Pythagorean Theorem for a right triangle with legs a and b and hypotenuse c.

a² + b² = c²

What is the distance formula between points (x₁, y₁) and (x₂, y₂)?

d = √[(x₂ − x₁)² + (y₂ − y₁)²]

What is the midpoint of the segment connecting (x₁, y₁) and (x₂, y₂)?

((x₁ + x₂)/2 , (y₁ + y₂)/2)

How do you calculate the slope between two points (x₁, y₁) and (x₂, y₂)?

m = (y₂ − y₁) ⁄ (x₂ − x₁)

What is the point-slope form of the equation of a line through (x₁, y₁) with slope m?

y − y₁ = m(x − x₁)

What is the slope-intercept form of a line?

y = mx + b

What is the standard form of a linear equation?

Ax + By = C