Area and Perimeter
Every shape has its area and perimeter. There is a different formula for area and perimeter of every shape as it has a different measurement. So before learning the area and perimeter formulas for all shapes. let’s learn the definition of Area and perimeter.
The area is the measurement of space enclosed by a closed geometric figure. Like the perimeter formula, there is also a set of area formula for polygons that can be represented using algebraic expressions.
For example, if you want to know the area of a square box with side 40 cm, You will use the formula:
Area of Square = a2, where a is the side of the square.
Similarly, The area of a triangle can also be found using its Area formula (1/2 × b ×h).
A Perimeter is the length of the boundary of a closed geometric figure. There is a set perimeter formula which simplifies your task of calculation. Algebraic expressions can be used to represent the perimeter formula for the regular polygons. Say that the length of each side of a regular polygon is l. The perimeter of shapes formula for each of the polygon can be given using the same variable l.
Example: To find the perimeter of a rectangular box, with length as 6cm and Breadth as 4 cm, we need to use the formula,
Perimeter of a Rectangle = 2 (L+B) = 2 ( 6 cm + 4 cm) = 2 × 10 cm = 20cm.
Area and Perimeter Formula Chart
|Geometric Shape||Perimeter Formula||Metrics|
|Parallelogram||2(Base + Height)|
|Triangle||A + b + c||a , b and c being the side lengths|
|Rectangle||2(Length + Width)|
|Square||4a||a =Length of a side|
|Trapezoid||a +b+c+d||A, b, c, d being the sides of the trapezoid|
|Kite||2a + 2b||a = Length of first pair
b = Length of second pair
|Rhombus||4 x a||a = Length of a side|
|Hexagon||6 x a||a = Length of a side|
List of Formulas
|Area = l × w||l = length
w = width
|Area of Square||Area = a2||a = sides of square|
|Area of a Triangle||Area = 1/2 bh||b = base
h = height
|Area of a Circle||Area = πr2||r= radius of the circle|
|Area of a Trapezoid||Area = 1/2 (a + b)h||a =base 1
b = base 2
h = vertical height
|Area of Ellipse||Area = πab||a = radius of the major axis
b = area of the minor axis
Perimeter and area of Equilateral triangle.
An Equilateral triangle is the one having all the three sides equal. To find its perimeter and area we need to know all the three sides of it.
- The perimeter of an equilateral triangle = 3 x length of a side = 3l.
- Area of an equilateral triangle = √3 / 4 a2
Perimeter and area of Square
A square is a shape with all the four sides equal in length. These four sides are also parallel to each other. They also make an angle of 90° with each other. To find the area and perimeter of the square, we need to know the measurement of one side of the square.
- Area of a square = 4 l2, Where l is the length of each side.
Similarly, the perimeter of a square = 4l.
Area and Perimeter is a very important topic in math and students are advised to refer NCERT solutions for better understanding and preparation. BYJU’S brings you NCERT solutions for – Perimeter and Area.