Geometry stands as a cornerstone of mathematics, weaving through the fabric of our spatial understanding and serving as a foundation for everything from architectural marvels to the design of everyday objects. This discipline invites us to explore the properties and relations of points, lines, angles, surfaces, and solids in two-dimensional and three-dimensional spaces. From calculating the area of a simple square to unraveling the complexities of spherical volumes, geometry equips us with the tools to measure, understand, and manipulate our physical world. 
 

List of all Geometric Formulas:

• Perimeter of a Square: To find the perimeter (P) of a square, multiply the length of one side (a) by 4. So, P = 4 * a.
• Area of a Square: The area (A) is found by squaring the length of one side (a), thus A = a^2.
• Perimeter of a Rectangle: The perimeter (P) is calculated by adding the length (l) and width (w) together and then multiplying by 2. Hence, P = 2 * (l + w).
• Area of a Rectangle: Multiply the length (l) by the width (w) to get the area (A), so A = l * w.
• Circumference of a Circle: The circumference (C) can be found using the radius (r) with C = 2 * π * r. Alternatively, using the diameter (d), C = π * d.
• Area of a Circle: Use the radius (r) to calculate the area (A) with the formula A = π * r^2.
• Surface Area of a Sphere: With the radius (r), the surface area (A) is 4 * π * r^2.
• Volume of a Sphere: The volume (V) uses the radius (r) in the formula V = 4/3 * π * r^3.
• Surface Area of a Cylinder: To find the surface area (A) of a cylinder, use the radius (r) and height (h) in A = 2 * π * r * (h + r).
• Volume of a Cylinder: The volume (V) is found with the radius (r) and height (h) as V = π * r^2 * h.
• Surface Area of a Cube: For a cube with side length (a), the surface area (A) is 6 * a^2.
• Volume of a Cube: The volume (V) of a cube is the cube of its side length (a), so V = a^3.
• Surface Area of a Rectangular Prism: It is calculated by adding the areas of all six faces, using the length (l), width (w), and height (h) in the formula A = 2 * (lw + lh + wh).
• Volume of a Rectangular Prism: The volume (V) is found by multiplying the length (l), width (w), and height (h) together, thus V = l * w * h.
• Volume of a Cone: Use the radius of the base (r) and height (h) in the formula V = 1/3 * π * r^2 * h for the volume.
• Surface Area of a Cone: The surface area (A) includes the base and the side, calculated as A = π * r * (r + sqrt(h^2 + r^2)).
• Pythagorean Theorem: In a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b), so c^2 = a^2 + b^2.
• Area of a Triangle: The area (A) can be found with the base (b) and height (h) using A = 1/2 * b * h.
• Area of a Parallelogram: Similar to a rectangle, the area (A) is the base (b) times the height (h), thus A = b * h.
• Area of a Trapezoid: With bases (a and b) and height (h), the area (A) is A = 1/2 * (a + b) * h.
• Volume of a Pyramid: The volume (V) is one-third the product of the base area (B) and height (h), so V = 1/3 * B * h.