Geometric Formulas for Area and Volume

This page presents essential formulas for area and volume of solids, focusing on both two-dimensional shapes and three-dimensional objects. It serves as a comprehensive guide for calculating aire des figures géométriques (area of geometric figures) and volumes of various solids.

The page is divided into two main sections: Aires (Areas) and Volumes. Each section provides formulas and visual representations of different geometric shapes.

In the Aires section, formulas are given for:

• Square: A = c × c (where c is the side length)
• Rectangle: A = l × L (where l is width and L is length)
• Right-angled triangle: A = (l × L) ÷ 2
• Any triangle: A = (base × height) ÷ 2
• Circle: A = π × r² (where r is the radius)

The Volumes section explains that volume is the measure of a solid's interior. It distinguishes between two types of solids:

1. Solids without a point (e.g., cuboid, cube, cylinder): V = base area × height
2. Solids with a point (e.g., cone, pyramid): V = (1/3) × base area × height

Definition: Volume is defined as the measure of the interior of a solid.

Highlight: The document emphasizes that volume is related to the capacity of a solid.

Vocabulary: The unit of volume introduced is the cubic decimeter (dm³).

Example: A practical example is provided, showing the calculation of a cuboid's volume: V = base × height = (4 × 4) × 6 = 16 × 6 = 96 cm³

Highlight: An important relationship is noted: 1 L = 1 dm³, connecting volume units to liquid measurements.

This page serves as a valuable reference for students learning geometry, providing a concise yet comprehensive overview of aire et volume formules (area and volume formulas) for various shapes and solids.