Area formulas in mathematics are mathematical expressions used to calculate the amount of surface enclosed within a two-dimensional shape. It is generally measured in square units, such as cm², m², or km².
Area is measured in square units. The SI unit to measure the area is m2.
2D Shapes
2D (Two-Dimensional) shapes are flat figures that have only two dimensions: length and breadth (or width). They do not have any thickness. Some common 2D shapes are rectangle, square, triangle, circle, parallelogram, rhombus, trapezoid, and ellipse.
The area of a 2D shape is the amount of space enclosed within its boundary. Different shapes have different formulas to calculate their area.
Area of a Rectangle
A rectangle is a four-sided figure in which opposite sides are equal and parallel, and all four angles are 90°.
Formula: Area of Rectangle (A) = Length × Breadth = l × b
where,
- l = length
- b = breadth
Area of a Square
A square is a four-sided figure in which all sides are equal and each angle measures 90°.
Formula: Area of Square (A) = a²
where,
- a = length of one side
Area Formula of a Triangle
A triangle is a polygon with three sides and three angles. Its area depends on its base and height.
Formula: Area of Triangle (A) = ½ × b × h
where,
- b = base
- h = height
Area of a Circle
A circle is a closed curve in which every point on the boundary is at the same distance from a fixed point called the center. This fixed distance is called the radius.
Formula: Area of Circle (A) = πr²
where,
- r = radius
- π ≈ 3.14 or 22/7
Area of a Parallelogram
A parallelogram is a four-sided figure in which opposite sides are equal and parallel.
Formula: Area of Parallelogram (A) = b × h
where,
- b = base
- h = perpendicular height
Area of a Rhombus
A rhombus is a quadrilateral with all four sides equal. Its opposite sides are parallel, but its angles are not necessarily equal.
Formula: Area of Rhombus (A) = ½ × d₁ × d₂
where,
- d₁ = first diagonal
- d₂ = second diagonal
Area of a Trapezoid (Trapezium)
A trapezoid (or trapezium) is a quadrilateral with one pair of opposite sides parallel.
Formula: Area of Trapezoid (A) = ½(a + b)h
where,
- a and b = lengths of the parallel sides
- h = height
Area of an Ellipse
An ellipse is a closed curve formed by two axes called the major axis and minor axis.
Formula: Area of Ellipse (A) = πab
where,
- a = semi-major axis
- b = semi-minor axis
Area of a Semicircle
A semicircle is half of a circle formed by dividing a circle along its diameter.
Formula: Area of Semicircle (A) = ½πr²
where,
- r = radius
Note: The correct formula for the area of a semicircle is ½πr², not ¼πr². The formula ¼πr² is incorrect for the area of a semicircle.