Geometry Formulas Flashcards
Free geometry formulas flashcards for perimeter, area, circle formulas, volume, surface area, angle rules, the Pythagorean theorem and coordinate geometry. Flip to check each formula, then keep drilling the ones you miss.
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How to study with these geometry formulas flashcards
- Read the front of the card and say or write your answer before you flip it.
- Flip the card, then mark I know this only if you were right without hesitating.
- Mark Review again for anything you missed, then use Review missed only to drill those cards.
- Pick one topic at a time, then shuffle all topics for a mixed review.
All 51 cards at a glance
Every card is also listed below so you can scan, print or review without the viewer.
Perimeter and area
| Question | Answer |
|---|---|
| Area of a rectangle? | A = l × w |
| Perimeter of a rectangle? | P = 2l + 2w |
| Area of a square with side s? | A = s² |
| Perimeter of a square? | P = 4s |
| Area of a triangle? | A = ½ × b × h |
| Area of a parallelogram? | A = b × h |
| Area of a trapezoid? | A = ½(b₁ + b₂)h |
| Area of a rhombus from its diagonals? | A = ½ × d₁ × d₂ |
| Area of an equilateral triangle with side s? | A = (√3 / 4) s² |
| Heron’s formula (sides a, b, c, s = half the perimeter)? | A = √[s(s − a)(s − b)(s − c)] |
Circles
| Question | Answer |
|---|---|
| Circumference of a circle? | C = 2πr = πd |
| Area of a circle? | A = πr² |
| Arc length for a central angle θ in degrees? | (θ/360) × 2πr |
| Area of a sector with central angle θ in degrees? | (θ/360) × πr² |
| Arc length for θ in radians? | s = rθ |
| Area of a sector with θ in radians? | A = ½r²θ |
| How does the diameter relate to the radius? | d = 2r |
| Inscribed angle versus its intercepted arc? | The angle is half the arc. |
| Central angle versus its arc? | The angle equals the arc. |
Volume
| Question | Answer |
|---|---|
| Volume of a rectangular prism? | V = l × w × h |
| Volume of a cube? | V = s³ |
| Volume of any prism or cylinder? | V = (area of base) × height |
| Volume of a cylinder? | V = πr²h |
| Volume of a cone? | V = ⅓πr²h |
| Volume of a pyramid? | V = ⅓ × (area of base) × h |
| Volume of a sphere? | V = 4/3 πr³ |
Surface area
| Question | Answer |
|---|---|
| Surface area of a cube? | SA = 6s² |
| Surface area of a rectangular prism? | SA = 2(lw + lh + wh) |
| Surface area of a sphere? | SA = 4πr² |
| Total surface area of a cylinder? | SA = 2πr² + 2πrh |
| Lateral area of a cylinder? | L = 2πrh |
| Lateral area of a cone with slant height ℓ? | L = πrℓ |
| Total surface area of a cone? | SA = πr² + πrℓ |
Angles and polygons
| Question | Answer |
|---|---|
| Sum of the interior angles of a triangle? | 180° |
| Sum of the interior angles of an n-sided polygon? | (n − 2) × 180° |
| Each interior angle of a regular n-gon? | (n − 2) × 180° / n |
| Sum of the exterior angles of any convex polygon? | 360° |
| Complementary angles add to? | 90° |
| Supplementary angles add to? | 180° |
| Exterior angle of a triangle equals? | The sum of the two remote interior angles. |
| Vertical angles are? | Equal in measure. |
| Triangle inequality? | The sum of any two sides is greater than the third side. |
Right triangles and coordinates
| Question | Answer |
|---|---|
| Pythagorean theorem? | a² + b² = c² (c is the hypotenuse) |
| Sides of a 45-45-90 triangle? | x : x : x√2 |
| Sides of a 30-60-90 triangle? | x : x√3 : 2x (short leg : long leg : hypotenuse) |
| Distance between (x₁, y₁) and (x₂, y₂)? | d = √[(x₂ − x₁)² + (y₂ − y₁)²] |
| Midpoint of two points? | ((x₁ + x₂)/2, (y₁ + y₂)/2) |
| Slope between two points? | m = (y₂ − y₁) / (x₂ − x₁) |
| Slopes of parallel lines? | Equal |
| Slopes of perpendicular lines? | Negative reciprocals (product is −1) |
| Equation of a circle with center (h, k) and radius r? | (x − h)² + (y − k)² = r² |
Frequently asked questions
Which geometry formulas are given on the SAT or ACT?
The SAT reference sheet gives area, circumference, volume and special right triangle facts. The ACT does not give a formula sheet. Check the current test instructions.
What is the difference between area and perimeter?
Perimeter is the distance around a shape and uses units like cm. Area is the space inside and uses square units like cm².
Why does the cone volume have a one-third?
A cone holds exactly one third of the volume of a cylinder with the same base and height.
Sources
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