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geometric formula sheet
Guri Bee
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geometric formula sheet

2 min read 21-10-2024
geometric formula sheet

Your Guide to Geometric Formulas: A Comprehensive Cheat Sheet

Geometry can feel like a world of shapes and angles, but with the right tools, it becomes a fascinating journey of understanding the world around us. This article provides a comprehensive cheat sheet of essential geometric formulas, making navigating this world a breeze.

Let's dive in, starting with the basics:

1. Area and Perimeter

  • Area: The space a shape occupies.
  • Perimeter: The total length of the boundary of a shape.

Common Shapes and Their Formulas:

Shape Area Formula Perimeter Formula
Square A = s² (where s is the side length) P = 4s
Rectangle A = l × w (where l is the length and w is the width) P = 2(l + w)
Triangle A = (1/2) × b × h (where b is the base and h is the height) P = a + b + c (where a, b, and c are the side lengths)
Circle A = πr² (where r is the radius) C = 2πr (where C is the circumference)

Example:

  • You have a square garden with sides of 5 meters. To find the area you'd use: A = s² = 5² = 25 square meters.
  • To build a fence around it, you'd need: P = 4s = 4 × 5 = 20 meters of fencing.

2. Volume and Surface Area

  • Volume: The amount of space a three-dimensional object occupies.
  • Surface Area: The total area of all the surfaces of a three-dimensional object.

Common Shapes and Their Formulas:

Shape Volume Formula Surface Area Formula
Cube V = s³ (where s is the side length) SA = 6s²
Rectangular Prism V = l × w × h (where l is the length, w is the width, and h is the height) SA = 2(lw + lh + wh)
Sphere V = (4/3)πr³ (where r is the radius) SA = 4πr²
Cylinder V = πr²h (where r is the radius and h is the height) SA = 2πrh + 2πr²
Cone V = (1/3)πr²h (where r is the radius and h is the height) SA = πr² + πrl (where l is the slant height)

Example:

  • To find the volume of a cylindrical water tank with a radius of 2 meters and a height of 5 meters, you'd use: V = πr²h = π × 2² × 5 = 20π cubic meters.

3. Pythagoras Theorem

This theorem relates the sides of a right-angled triangle.

  • Formula: a² + b² = c² (where a and b are the lengths of the legs and c is the length of the hypotenuse).

Example:

  • You have a right-angled triangle with legs measuring 3 and 4 meters. To find the hypotenuse, you'd use: c² = a² + b² = 3² + 4² = 9 + 16 = 25. Therefore, c = √25 = 5 meters.

4. Trigonometry: SO-H CAH TOA

  • Sine (Sin): Opposite side / Hypotenuse
  • Cosine (Cos): Adjacent side / Hypotenuse
  • Tangent (Tan): Opposite side / Adjacent side

Example:

  • In a right-angled triangle with an angle of 30 degrees, the opposite side is 5 meters and the adjacent side is 8.66 meters. You can find the sine of the angle as: Sin(30°) = 5/10 = 0.5.

Remember: This cheat sheet is just the beginning. There are many other geometric formulas and concepts to explore. Websites like Khan Academy and Math is Fun offer excellent resources to learn more.

Additional Value:

  • Real-World Applications: Geometry is more than just formulas. It's used in architecture, engineering, design, and even art!
  • Visual Learning: Look for visual explanations and diagrams to help you understand these formulas.
  • Practice Makes Perfect: Work through examples and exercises to solidify your understanding.

Keywords: Geometric formulas, area, perimeter, volume, surface area, Pythagoras theorem, trigonometry, SO-H CAH TOA, cheat sheet, math, geometry.

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