Area of 2D Shapes Formulas
This document provides formulas for calculating the area of common two-dimensional (2D) shapes.
What is Area?
Area is the amount of space a two-dimensional shape covers. It is measured in square units, such as square centimeters (cm²) or square inches (in²).
Formulas for Common 2D Shapes:
1. Square
- Formula: Area = side * side
- Where:
- side = length of one side of the square
2. Rectangle
- Formula: Area = length * width
- Where:
- length = length of the rectangle
- width = width of the rectangle
3. Triangle
- Formula: Area = (1/2) * base * height
- Where:
- base = length of the base of the triangle
- height = perpendicular distance from the base to the opposite vertex
4. Parallelogram
- Formula: Area = base * height
- Where:
- base = length of the base of the parallelogram
- height = perpendicular distance between the base and the opposite side
5. Trapezoid
- Formula: Area = (1/2) * (base1 + base2) * height
- Where:
- base1 = length of one base of the trapezoid
- base2 = length of the other base of the trapezoid
- height = perpendicular distance between the two bases
6. Circle
- Formula: Area = π * radius²
- Where:
- π (pi) ≈ 3.14159
- radius = distance from the center of the circle to any point on the circumference
7. Ellipse
- Formula: Area = π * a * b
- Where:
- π (pi) ≈ 3.14159
- a = length of the semi-major axis
- b = length of the semi-minor axis
8. Regular Polygon
- Formula: Area = (1/2) * perimeter * apothem
- Where:
- perimeter = total length of all sides of the polygon
- apothem = distance from the center of the polygon to the midpoint of a side
Example:
Calculate the area of a rectangle with a length of 8 cm and a width of 5 cm.
- Area = length * width
- Area = 8 cm * 5 cm
- Area = 40 cm²
Using the Formulas
- Identify the shape.
- Measure the required dimensions.
- Substitute the values into the appropriate formula.
- Calculate the area.
By using these formulas, you can easily calculate the area of various 2D shapes.
