Geometry encompasses various shapes and figures, each with its own formula for calculating area. Here are some common geometric shapes and their respective area formulas:
1. Rectangle:
- Area = Length × Width
\[A = l × w\]
2. Square:
- Area = Side × Side (since all sides are equal)
\[Area = s² \]
3. Triangle:
\[Area =\frac{ (Base × Height)}{ 2}\]
\[A =\frac{ (b × h)}{ 2}\]
4. Circle:
\[Area = π × Radius²\]
\[A = πr²\]
5. Trapezoid:
- \[Area =\frac{ (Sum \ of \ the \ lengths \ of \ parallel \ sides) }{2} × Height\]
- \[A = \frac{(a + b) }{ 2} × h\]
6. Parallelogram:
- Area = Base × Height
- \[A = b × h\]
7. Ellipse:
- Area = π × Major Radius × Minor Radius
\[A = πab\]
8. Regular Polygon (with apothem):
- \[Area = \frac{(Perimeter × Apothem) }{2}\]
- \[A = \frac{(P × a) }{2}\]
9. Sector of a Circle:
- \[Area = \frac{θ}{360} × πr²\]
- \[A =\frac{θ}{360} × πr² \](where θ is the central angle in degrees)
10. Rhombus:
- \[Area = \frac{(Diagonal₁ × Diagonal₂) }{ 2}\]
- \[A = \frac{(d₁ × d₂) }{2}\]
11. Equilateral Triangle:
- \[Area = Side² × \frac{\sqrt3}{ 4}\]
- \[A =\frac{ \sqrt{3}}{ 4}s^2\]
These are some of the most commonly used area formulas in geometry. Remember to use the appropriate units for measurements to get the area in the desired units (e.g., square meters, square inches, etc.).
