Geometry Formulas Flashcards: Area, Perimeter, Volume and More
35 cards · free to study, print and copy
Geometry Formulas Flashcards: Area, Perimeter, Volume and More
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About this deck
This deck collects the geometry formulas students use most from middle school through high school geometry: area and perimeter of plane shapes, volume and surface area of solids, angle sums, the Pythagorean theorem, and the distance, midpoint and slope formulas.
The front names the quantity (for example "Area of a trapezoid"); the back gives the formula and what each letter stands for. Letters follow common textbook conventions: r for radius, h for height, b for base, l and w for length and width.
It is a good review before unit tests, the SAT or ACT math sections, or any exam where a formula sheet is not provided.
Study tips
- Say what the formula means, not just the symbols: "area of a triangle is half of base times height."
- Group related formulas: circle area and circumference together, cylinder volume right after circle area.
- Sketch the shape on scratch paper before flipping the card; drawing is a strong memory cue.
- Check units: area is squared (cm²), volume is cubed (cm³). A wrong unit often reveals a wrong formula.
All 35 cards
| Front | Back |
|---|---|
| Area of a rectangle | A = l × w (length × width) |
| Perimeter of a rectangle | P = 2l + 2w |
| Area of a square | A = s² (s = side length) |
| Area of a triangle | A = ½ × b × h (base × height ÷ 2) |
| Area of a parallelogram | A = b × h (h is perpendicular to the base) |
| Area of a trapezoid | A = ½ × (b₁ + b₂) × h |
| Area of a rhombus (using diagonals) | A = ½ × d₁ × d₂ |
| Area of a circle | A = πr² |
| Circumference of a circle | C = 2πr = πd |
| Arc length (angle θ in degrees) | L = (θ/360) × 2πr |
| Area of a sector (angle θ in degrees) | A = (θ/360) × πr² |
| Pythagorean theorem | a² + b² = c² (c = hypotenuse of a right triangle) |
| Sum of interior angles of a triangle | 180° |
| Sum of interior angles of an n-sided polygon | (n − 2) × 180° |
| Each interior angle of a regular n-gon | (n − 2) × 180° ÷ n |
| Sum of exterior angles of any convex polygon | 360° |
| Volume of a rectangular prism | V = l × w × h |
| Surface area of a rectangular prism | SA = 2lw + 2lh + 2wh |
| Volume of a cube | V = s³ |
| Surface area of a cube | SA = 6s² |
| Volume of a cylinder | V = πr²h |
| Surface area of a cylinder | SA = 2πr² + 2πrh |
| Volume of a cone | V = ⅓πr²h |
| Surface area of a cone | SA = πr² + πrl (l = slant height) |
| Volume of a sphere | V = ⁴⁄₃πr³ |
| Surface area of a sphere | SA = 4πr² |
| Volume of a pyramid | V = ⅓ × B × h (B = area of the base) |
| Volume of any prism | V = B × h (B = area of the base) |
| Distance between two points | d = √((x₂ − x₁)² + (y₂ − y₁)²) |
| Midpoint of a segment | ((x₁ + x₂)/2, (y₁ + y₂)/2) |
| Slope of a line | m = (y₂ − y₁) / (x₂ − x₁) |
| Slope-intercept form | y = mx + b (m = slope, b = y-intercept) |
| Equation of a circle | (x − h)² + (y − k)² = r², center (h, k) |
| Side ratios of a 30-60-90 triangle | 1 : √3 : 2 |
| Side ratios of a 45-45-90 triangle | 1 : 1 : √2 |
Frequently asked questions
›Is π exactly 3.14?
No. π is irrational, about 3.14159. Use 3.14 or 22/7 only when a problem tells you to.
›What is the difference between slant height and height?
Height (h) is measured straight up from the base at a right angle. Slant height (l) runs along the side face of a cone or pyramid.
›Do I need to memorize these for the SAT?
The SAT provides a reference sheet with several of these formulas, but knowing them saves time. The ACT does not provide a formula sheet.
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