Table of Contents
Area
Area Formulas
Square
\[
\text{Area of a Square} = \text{side}^2
\]
Rectangle
\[
\text{Area of a Rectangle} = \text{length} \times \text{breadth}
\]
Triangle
\[
\text{Area of a Triangle} = \frac{1}{2} \times \text{base} \times \text{height}
\]
For a triangle with sides \(a\), \(b\), and \(c\), and semi-perimeter \(s = \frac{a + b + c}{2}\):
\[ \text{Area} = \sqrt{s(s - a)(s - b)(s - c)} \]Parallelogram
\[
\text{Area of a Parallelogram} = \text{base} \times \text{height}
\]
Trapezium
\[
\text{Area of a Trapezium} = \frac{1}{2} \times (\text{sum of parallel sides}) \times \text{height}
\]
Circle
\[
\text{Area of a Circle} = \pi \times \text{radius}^2
\]
Ellipse
\[
\text{Area of an Ellipse} = \pi \times \text{semi-major axis} \times \text{semi-minor axis}
\]
Sector of a Circle
\[
\text{Area of a Sector} = \frac{\theta}{360} \times \pi \times \text{radius}^2
\]
where \(\theta\) is the central angle in degrees.
Rhombus
\[
\text{Area of a Rhombus} = \frac{1}{2} \times \text{diagonal}_1 \times \text{diagonal}_2
\]
Polygon
For a regular polygon with \(n\) sides of length \(a\) and apothem \(a_p\):
\[ \text{Area} = \frac{1}{2} \times n \times a \times a_p \]
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