About this Flash Card Set
20 Cards
by ryan_mitchell
A quick-reference deck of the essential geometry formulas for area, perimeter, and volume, with every variable defined so students can apply them with confidence.
Front
Area of a rectangle
Back
length × width (l = length, w = width).
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Front
Area of a square
Back
side × side, or s² (s = side length).
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Front
Area of a triangle
Back
½ × base × height, or (b × h) / 2 (b = base, h = perpendicular height).
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Front
Area of a circle
Back
π × r² (r = radius; π ≈ 3.14159).
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Front
Area of a trapezoid
Back
½ × (b₁ + b₂) × h (b₁ and b₂ = the two parallel sides, h = height between them).
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Front
Area of a parallelogram
Back
base × height, or b × h (b = base, h = perpendicular height, not the slanted side).
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Front
Circumference of a circle
Back
2 × π × r, or π × d (r = radius, d = diameter; π ≈ 3.14159).
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Front
Perimeter of a rectangle
Back
2 × (length + width), or 2l + 2w (l = length, w = width).
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Front
Perimeter of any polygon
Back
The sum of the lengths of all its sides — just add every side together.
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Front
Volume of a cube
Back
side × side × side, or s³ (s = edge length).
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Front
Volume of a rectangular prism
Back
length × width × height, or l × w × h.
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Front
Volume of a cylinder
Back
π × r² × h (r = radius of the circular base, h = height).
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Front
Volume of a cone
Back
⅓ × π × r² × h (r = radius of the base, h = height). It is one-third of a cylinder with the same base and height.
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Front
Volume of a sphere
Back
(4/3) × π × r³ (r = radius).
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Front
The Pythagorean theorem
Back
For a right triangle, a² + b² = c² (a and b = the two legs, c = the hypotenuse, the side opposite the right angle). Example: 3² + 4² = 5².
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Front
Sum of the interior angles of a triangle
Back
Always 180 degrees, for every triangle. Example: if two angles are 90° and 60°, the third is 30°.
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Front
Area of a triangle given base and height
Back
½ × base × height. Example: a triangle with base 6 and height 4 has area ½ × 6 × 4 = 12.
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Front
Radius vs. diameter of a circle
Back
The radius (r) reaches from the center to the edge; the diameter (d) crosses the whole circle through the center. The diameter is twice the radius: d = 2r.
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Front
Surface area of a cube
Back
6 × s² (s = edge length), since a cube has 6 identical square faces.
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Front
Volume — what does it measure?
Back
The amount of space a 3-D solid takes up, measured in cubic units (like cm³ or in³). Area, by contrast, measures a flat 2-D surface in square units.
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