When we explore geometric shapes, there are two main types to know: regular shapes and irregular shapes. This difference changes how we find area and perimeter.

Regular Shapes:

• Regular shapes have equal sides and angles. Examples include a square and an equilateral triangle.
• To find the perimeter of a regular shape, you can use simple formulas:
  • For a square with side length (s): The perimeter (P = 4s).
  • For an equilateral triangle with side length (a): The perimeter (P = 3a).
• To find the area:
  • The area of a square is (A = s \times s) or (A = s^2).
  • The area of an equilateral triangle is (A = \frac{\sqrt{3}}{4}a^2). (But don't worry if that looks complicated; we’ll stick to simple shapes here!)

Irregular Shapes:

• Irregular shapes don’t have equal sides or angles. This makes finding their area and perimeter a bit harder. Think of a trapezium or any odd shape.
• To calculate the perimeter, just add up the lengths of all the sides:
  • If a shape has sides (a), (b), (c), and (d): The perimeter (P = a + b + c + d).
• Finding the area can vary depending on the shape. For example:
  • For a trapezium, you can use this formula: $A = \frac{(b_1 + b_2) \times h}{2}$ Here, (b_1) and (b_2) are the lengths of the two bases, and (h) is the height.

In short, regular shapes are easier to work with because of their equal sides and angles. For irregular shapes, you need to think a bit more and use different methods to find their area and perimeter.