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.
