Important Maths Formulas | Area Formulas

Area of a Circle Formula = ?r²
where
r – radius of a circle
Area of a Triangle Formula A=\( \frac{1}{2} b h \)
where
b – base of a triangle.
h – height of a triangle.


Area of Equilateral Triangle Formula = \( \frac{\sqrt{3}}{4} s^{2} \)
where
s is the length of any side of the triangle.


Area of Isosceles Triangle Formula = \( \frac{1}{2} b h \)


where:
a be the measure of the equal sides of an isosceles triangle.
b be the base of the isosceles triangle.
h be the altitude of the isosceles triangle.
Area of a Square Formula = a²


Area of a Rectangle Formula = L. B
where
L  is the length.
B is the Breadth.
Area of a Pentagon Formula = \( \frac{5}{2} s . a \)
Where,
s is the side of the pentagon.
a is the apothem length.


Area of a Hexagon Formula = \(\frac{3 \sqrt{3}}{2} x^{2} \)
where
where “x” denotes the sides of the hexagon.



Area of a Hexagon Formula = \(\frac{3}{2} . d . t \)
Where “t” is the length of each side of the hexagon and “d” is the height of the hexagon when it is made to lie on one of the bases of it.
Area of an Octagon Formula = \( 2 a^{2}(1+\sqrt{2}) \)
Consider a regular octagon with each side “a” units.


Area of Regular Polygon Formula:
By definition, all sides of a regular polygon are equal in length. If you know the length of one of the sides, the area is given by the formula:

where
s  is the length of any side
n  is the number of sides
tan  is the tangent function calculated in degrees



Area of a Parallelogram Formula = b . a
where
b is the length of any base
a is the corresponding altitude

Area of Parallelogram: The number of square units it takes to completely fill a parallelogram.
Formula: Base × Altitude

Area of a Rhombus Formula = b . a
where
b is the length of the base
a is the altitude (height).


Area of a Trapezoid Formula = The number of square units it takes to completely fill a trapezoid.
Formula: Average width × Altitude


The area of a trapezoid is given by the formula

where
b1, b2 are the lengths of each base
h is the altitude (height)


Area of a Sector Formula (or) Area of a Sector of a Circle Formula =  \(\pi r^{2}\left(\frac{C}{360}\right) \)
where:
C is the central angle in degrees
r is the radius of the circle of which the sector is part.
? is Pi, approximately 3.142

Sector Area – The number of square units it takes to exactly fill a sector of a circle.
Area of a Segment of a Circle Formula

Area of a Segment in Radians \(A =1 / 2 \times r^{2}(\theta-\sin \theta) \)

Area of a Segment in Degrees \(A =\frac{1}{2} r^{2}\left(\frac{\pi}{180} \theta-\sin \theta\right) \)

Area of a Segment of a Circle Formula
Area under the Curve Formula:
The area under a curve between two points is found out by doing a definite integral between the two points. To find the area under the curve y = f(x) between x = a & x = b, integrate y = f(x) between the limits of a and b. This area can be calculated using integration with given limits.