Geometric Shapes and Formulas

Geometric Shapes

• Circle:

  • Area formula: A = πr², where r is the radius.
  • Circumference formula: C = 2πr, measuring the distance around the circle.

• Square:

  • Area calculation: A = length x length, which simplifies to A = a².
  • Perimeter formula: P = 4a, representing the total distance around the square.

• Rectangle:

  • Area is determined by A = length x breadth, represented as A = ab.
  • Perimeter is calculated using P = 2a + 2b, accounting for both lengths and widths.

3D Shapes

• Right Cylinder:

  • Volume is calculated with the formula V = πr² x h, where r is the radius and h is height.
  • Surface area is given by SA = 2πr² + 2πrh, covering top, bottom, and the curved surface area.

• Square Prism (Cube):

  • Volume formula: V = a² x H, noting that height (H) equals side length (a) if square.
  • Simplified volume: V = a³.
  • Surface area: SA = 6a², reflecting all six square faces.

• Square Base Pyramid:

  • Volume calculated as V = 1/3 a² x H, where 'a' is the base side length and 'H' is the height.
  • Surface area: SA = area of square base (a²) + 4 times the area of a triangle side; simplifies to SA = a² + 2ah, with 'h' as the triangle height.

• Rectangular Prism (Cuboid):

  • Volume determined by V = l x b x h, multiplying length, breadth, and height.
  • Surface area formula: SA = 2lb + 2lh + 2bh, accounting for all six rectangular faces.

• Slant Height:

  • Defined as the line from the midpoint of the base edge to the apex of the pyramid.
  • Calculation uses Pythagorean Theorem, assessing the perpendicular height and base dimensions.