What is Area?
TThe area of a figure is the space that its boundary takes up. The unit square is used to measure it. m2 is the SI unit used to measure the area. In addition to being employed in many mathematical ideas, area is also used in practical situations, such as determining the area of a room, table, etc.
Area Formulas
In mathematics, area formulae are crucial tools for determining how much space various two-dimensional shapes enclose. The area of geometric shapes like squares, rectangles, circles, triangles, trapezoids, and ellipses can be calculated using these formulas. These formulas allow us to precisely determine the area of various forms, which helps us with significant computations and real-world issue solving.
Area Formulas of 2D Shapes
2-D shapes are those that only have two dimensions. They are depicted in two dimensions and rely on two parameters, usually width (b) and length (l). Among the several 2-D forms are triangles, circles, squares, rectangles, and others.
The formulas used to find the area of different 2D shapes, including the area of a triangle, square, rectangle, rhombus, etc., are known as area of 2D shapes formulas. In mathematics, these area formulas are widely employed to solve a variety of geometrical problems. Different area formulas for different shapes include
Area Formula of a Rectangle
Rectangle is a 2-Dimensional figure which is a quadrilateral, i.e. it has four sides its opposite sides are parallel and equal. All the angles in the rectangle are equal and their measure is 90 degrees. The diagonals of the rectangle are equal and they are perpendicular bisectors of each other.
The formula for calculating the area of a rectangle is with length and l and breadth b is, Area of Rectangle (A) = l×b square units
Area Formula of a Square
In two dimensions, a square is a quadrilateral, meaning that all four of its sides are equal and that its opposite sides are parallel. Every angle in the square has the same measure, which is 90 degrees. The square’s diagonals are equal and bisect one another perpendicularly.
The following formula can be used to get the area of a square with side a:
Area of Square (A) = a2 sq. units
Area Formula of a Triangle
The most basic polygon is a triangle, which is created by combining three straight lines. It is a polygon having three angles, as the name implies. The area of the triangle is the space inside its perimeter, and the perimeter is the total of the lengths of its sides.
The area of a triangle with base b and height h may be found using the following formula:
Area of Triangle (A) = 1/2 × bh sq. units
Area Formula of a Circle
A circle is a geometric shape that lacks a straight line. It is the location of the point that is consistently separated from the fixed point by a given distance. The radius of the circle is the fixed distance, and the fixed point is known as the circle’s center.
The following formula can be used to determine a circle’s area where r is its radius:
Area of Circle (A) = πr2 sq. units
Area Formula of a Parallelogram
Parallelogram is a 2-D figure in which the opposite sides are parallel and equal. The formula for calculating the area of parallelogram with base b and height h are,
Area of Parallelogram (A) = bh sq. units
Area Formula of a Rhombus
Rhombus is a quadrilateral with all four sides equal and parallel but not all angles are equal. The formula for calculating the area of rhombus with diagonal d1 and d2 are,
Area of Rhombus (A) = 1/2 × d1 × d2 sq. units
Area Formula of a Trapezoid
Trapezoid is another name of trapezium. It is a quadrilateral in which the opposite sides are parallel. The formula for calculating the area of trapezoid with parallel sides a and b and height h is,
Area of Trapezoid (A) = 1/2(a +b)h sq. units
Area Formula of a Ellipse
Ellipse is a 2-D shape and comes under conic sections. The formula for calculating the area of a ellipse with axis as a and b are,
Area of Ellipse (A) = πab sq. units
Area Formula of a Semicircle
Semicircle is a 2-D figure which is half of circle. The formula to calculate the area of semicircle with radius r is,
Area of Semicircle (A) = 1/4(πr2) sq. units
This is a guide for understanding the area of shapes. Hope it will help you.