Page 2: Areas of Plane Figures

This page comprehensively covers the formulas for calculating areas of various two-dimensional shapes.

Definition: Area is the amount of space taken up by a two-dimensional shape's surface.

Example: For a square with side length 5 units, the area would be 5 × 5 = 25 square units.

The following formulas are presented:

• Square: side × side
• Rectangle: length × width
• Triangle: (base × height) ÷ 2
• Parallelogram: base × height
• Rhombus: (diagonal₁ × diagonal₂) ÷ 2
• Circle: πr² (where π = 3.14)

Vocabulary: π (pi) is a mathematical constant approximately equal to 3.14, used in calculations involving circles.

Page 3: Volumes of Geometric Solids

This page details the formulas for calculating volumes of three-dimensional objects.

Definition: Volume is the amount of three-dimensional space occupied by a solid object.

The following volume formulas are presented:

• Cube: side³
• Right prism: base area × height
• Cylinder: base area × height
• Cone: (base area × height) ÷ 3
• Pyramid: (base area × height) ÷ 3
• Sphere: (4/3) × π × radius³

Highlight: Many three-dimensional shapes use the principle of base area multiplied by height, with some requiring division by 3 to account for tapering.

Example: For a cube with side length 2 units, the volume would be 2³ = 8 cubic units.

Page 1: Introduction to Mathematical Areas and Volumes

This introductory page sets up the foundation for understanding geometric calculations in mathematics, focusing on areas and volumes.

Definition: Areas and volumes are fundamental mathematical concepts used to measure two-dimensional spaces and three-dimensional objects respectively.

Highlight: The page serves as a title page introducing the main topics to be covered in the following sections.