Area of 2D Shapes: Formula Sheet
This document provides a comprehensive list of formulas for calculating the areas of common two-dimensional (2D) shapes.
1. Rectangle
Formula: Area = length × width
Where:
- length: The longer side of the rectangle.
- width: The shorter side of the rectangle.
Example: A rectangle with a length of 5 cm and a width of 3 cm has an area of 5 cm × 3 cm = 15 cm².
2. Square
Formula: Area = side²
Where:
- side: The length of any side of the square.
Example: A square with a side length of 4 cm has an area of 4 cm × 4 cm = 16 cm².
3. Triangle
Formula: Area = (1/2) × base × height
Where:
- base: The length of the side of the triangle that forms the bottom of the figure.
- height: The perpendicular distance from the base to the opposite vertex.
Example: A triangle with a base of 6 cm and a height of 4 cm has an area of (1/2) × 6 cm × 4 cm = 12 cm².
4. Circle
Formula: Area = π × radius²
Where:
- π (pi): A mathematical constant approximately equal to 3.14159.
- radius: The distance from the center of the circle to any point on its circumference.
Example: A circle with a radius of 5 cm has an area of π × 5 cm × 5 cm ≈ 78.54 cm².
5. Parallelogram
Formula: Area = base × height
Where:
- base: The length of any side of the parallelogram.
- height: The perpendicular distance between the base and the opposite side.
Example: A parallelogram with a base of 8 cm and a height of 3 cm has an area of 8 cm × 3 cm = 24 cm².
6. Trapezoid
Formula: Area = (1/2) × (base1 + base2) × height
Where:
- base1 and base2: The lengths of the two parallel sides of the trapezoid.
- height: The perpendicular distance between the two bases.
Example: A trapezoid with base1 = 6 cm, base2 = 4 cm, and height = 3 cm has an area of (1/2) × (6 cm + 4 cm) × 3 cm = 15 cm².
7. Rhombus
Formula: Area = (1/2) × diagonal1 × diagonal2
Where:
- diagonal1 and diagonal2: The lengths of the two diagonals of the rhombus.
Example: A rhombus with diagonal1 = 8 cm and diagonal2 = 6 cm has an area of (1/2) × 8 cm × 6 cm = 24 cm².
This formula sheet is a helpful resource for students and professionals who need to calculate the areas of 2D shapes. By understanding these formulas, you can confidently solve a wide range of area problems.
