Geometry: Area and Volume Calculation

Study Notes

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

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

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 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 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 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)