Geometry

• Circle


  The most fundamental shape in our universe, found in orbits of planets, wheels, and molecular structures
• Circle


  • All points are equal distance from the center
  • Radius is the distance from the center to the edge
• Diameter


  The distance across the widest part of the circle, equal to 2 times the radius
• Circumference


  The distance around the circle
• The ratio of the circumference to the diameter is a special number called pi (π)
• Pi (π) is approximately 3.14159 and continues infinitely without repeating
• Pi (π)


  The ratio of the circumference to the diameter of any circle
• Calculating circumference


  1. Circumference = π x diameter

  2. Circumference = 2 π x radius
• Calculating diameter from circumference

  Diameter = Circumference / π
• Calculating radius from diameter

  Radius = Diameter / 2
• Pi (π) is a fundamental and fascinating number that appears throughout mathematics and the universe
• Perimeter


  The distance around the outside of a shape
• Finding perimeter


  1. Add all the side lengths

  2. Identify any missing side lengths

  3. Use given information to calculate missing side lengths
• Area


  The amount of space or surface inside of a shape
• Finding area of composite shape

  1. Separate shape into simpler shapes

  2. Find area of each simpler shape

  3. Add the areas together to get total area
• Composite shape


  • Cannot easily find area using a single formula
  • Need to break it down into simpler shapes
• Simpler shapes used


  • Rectangle
  • Square
  • Triangle
• Area of rectangle = length x width
• Need to be careful to use the correct side lengths when calculating area
• Total area of composite shape = Area of part A + Area of part B
• Final area of the composite shape is 98 square feet
• Area


  The amount of surface something covers
• Finding the area of a rectangle

  1. Use the formula: area = length x width

  2. Plug in the length and width values

  3. Multiply to get the area
• Area is measured in square units
• Finding the area of a square

  1. Use the formula: area = side length squared

  2. Plug in the side length

  3. Square the side length to get the area
• Finding the area of a triangle

  1. Use the formula: area = 1/2 x base x height

  2. Plug in the base and height values

  3. Multiply and divide by 2 to get the area
• The area of a triangle is half the area of a parallelogram with the same base and height
• Finding the area of a circle


  1. Use the formula: area = π x radius squared

  2. Plug in the radius value

  3. Square the radius and multiply by π to get the area
• Diameter is the distance across a circle, and radius is half the diameter
• π is an irrational constant, often approximated as 3.14
• Area of a circle can be written in terms of π or as an approximate decimal value
• Finding the area of different shapes

  1. Rectangle

  2. Triangle (right, general, equilateral)

  3. Square

  4. Circle

  5. Sector of a circle

  6. Semicircle

  7. Parallelogram

  8. Trapezoid

  9. Rhombus

  10. Triangle (given two sides and included angle)

  11. Scalene triangle

  12. Square (given diagonal length)

  13. Circle with right triangle
• Rectangle area


  Length x Width
• Right triangle area


  1/2 x Base x Height
• General triangle area


  1/2 x Base x Height
• Equilateral triangle area


  √3/4 x Side^2
• Circle area


  π x Radius^2
• Sector of a circle area

  Angle (in degrees) / 360 x π x Radius^2
• Parallelogram area


  Base x Height
• Triangle area (given two sides and included angle)

  1/2 x Side1 x Side2 x sin(Angle)