Geometry: Area and Volume Calculation

Area Calculation

• Formulas:
  • Area of rectangle: A = l × w (where l is length and w is width)
  • Area of triangle: A = (b × h) / 2 (where b is base and h is height)
  • Area of circle: A = π × r^2 (where r is radius)
  • Area of parallelogram: A = b × h (where b is base and h is height)
• Units:
  • Square units: cm^2, m^2, km^2, etc.
  • Conversion between units: 1 m^2 = 100 cm^2 = 0.0001 km^2

Volume

• Formulas:
  • Volume of rectangular prism: V = l × w × h (where l is length, w is width, and h is height)
  • Volume of cylinder: V = π × r^2 × h (where r is radius and h is height)
  • Volume of sphere: V = (4/3) × π × r^3 (where r is radius)
• Units:
  • Cubic units: cm^3, m^3, km^3, etc.
  • Conversion between units: 1 m^3 = 1000 cm^3 = 0.001 km^3

Angles

• Types of angles:
  • Acute angle: Less than 90°
  • Right angle: Exactly 90°
  • Obtuse angle: Greater than 90° but less than 180°
  • Straight angle: Exactly 180°
  • Reflex angle: Greater than 180° but less than 360°
• Angle relationships:
  • Complementary angles: Sum of two angles is 90°
  • Supplementary angles: Sum of two angles is 180°
  • Vertical angles: Equal angles formed by two intersecting lines
• Angle measurement:
  • Degrees (°)
  • Radians (rad)

Area Calculation

• Area of rectangle is calculated by multiplying length and width: A = l × w
• Area of triangle is calculated by multiplying base and height, then dividing by 2: A = (b × h) / 2
• Area of circle is calculated by multiplying π with the square of the radius: A = π × r^2
• Area of parallelogram is calculated by multiplying base and height: A = b × h
• Area units include square centimeters (cm^2), square meters (m^2), square kilometers (km^2), and more
• Conversion between units: 1 m^2 = 100 cm^2 = 0.0001 km^2

Volume Calculation

• Volume of rectangular prism is calculated by multiplying length, width, and height: V = l × w × h
• Volume of cylinder is calculated by multiplying π with the square of the radius and the height: V = π × r^2 × h
• Volume of sphere is calculated by multiplying (4/3) with π, then multiplying the result with the cube of the radius: V = (4/3) × π × r^3
• Volume units include cubic centimeters (cm^3), cubic meters (m^3), cubic kilometers (km^3), and more
• Conversion between units: 1 m^3 = 1000 cm^3 = 0.001 km^3

Angles

• Angles can be classified into five types: acute, right, obtuse, straight, and reflex angles
• Acute angle is less than 90°
• Right angle is exactly 90°
• Obtuse angle is greater than 90° but less than 180°
• Straight angle is exactly 180°
• Reflex angle is greater than 180° but less than 360°
• Complementary angles sum up to 90°
• Supplementary angles sum up to 180°
• Vertical angles are equal angles formed by two intersecting lines
• Angles can be measured in degrees (°) or radians (rad)