## Area and Perimeter of 2D Shapes Formulas

This document provides a comprehensive guide to calculating the area and perimeter of various 2D shapes.

### What is Area?

**Area** is the amount of space a two-dimensional figure occupies. It is measured in square units, such as square centimeters (cm²) or square inches (in²).

### What is Perimeter?

**Perimeter** is the total distance around the outside of a two-dimensional figure. It is measured in linear units, such as centimeters (cm) or inches (in).

### Formulas for Area and Perimeter of Common 2D Shapes

Here are the formulas for calculating the area and perimeter of some common 2D shapes:

**1. Square**

**Area:**side * side (s²)**Perimeter:**4 * side (4s)

**2. Rectangle**

**Area:**length * width (l * w)**Perimeter:**2 * (length + width) (2l + 2w)

**3. Triangle**

**Area:**(1/2) * base * height (½bh)**Perimeter:**side1 + side2 + side3 (a + b + c)

**4. Circle**

**Area:**π * radius² (πr²)**Perimeter (Circumference):**2 * π * radius (2πr) or π * diameter (πd)

**Where:**

**π (pi)**is a mathematical constant approximately equal to 3.14159**s**is the side length of a square**l**is the length of a rectangle**w**is the width of a rectangle**b**is the base of a triangle**h**is the height of a triangle**r**is the radius of a circle**d**is the diameter of a circle

### Example Calculations

**Example 1: Square**

- Side length = 5 cm
- Area = s² = 5² = 25 cm²
- Perimeter = 4s = 4 * 5 = 20 cm

**Example 2: Circle**

- Radius = 7 cm
- Area = πr² = 3.14159 * 7² = 153.94 cm²
- Circumference = 2πr = 2 * 3.14159 * 7 = 43.98 cm

### Conclusion

Understanding the formulas for area and perimeter is crucial for solving various geometric problems. This document provides a comprehensive overview of these formulas and their application to common 2D shapes.