Area and Perimeter

The branch of mathematics that deals with the study of a geometric figure and its measurements such as area, perimeter, volume, the surface area is called Mensuration. 

Two-dimensional figures have two major properties that are:

• Area
• Perimeter

The region covered by a two-dimensional close figure is known as its area whereas the length covered by the boundary of a two-dimensional figure is known as the perimeter. 

Area

The unit of the region occupied by a two-dimensional closed figure or shape is called the area of the figure. The area of a closed plane figure is the measurement of the region i.e. surface, enclosed by its boundary or sides. The area is measured in square units that is square centimeter, square meter, square feet, square kilometer, etc. The area of a square with each side equal to 1 cm is taken to be 1 sq. cm, which is treated as a basic unit of measure. 

Square meter is generally written as m2 is the SI (international standard unit) unit for area. 

The formula for finding the area of various 2-dimensional shapes

• Area of a square 

Suppose there is a square with side s, then the area of square= s*s 

• Area of a rectangle 

Suppose a rectangle with its length be l and breath be b, then the area of rectangle= l*b 

• Area of triangle

suppose a triangle with its base b, and its height h (length of the perpendicular from the vertex opposite to its base is its height), the area of rectangle= ½*b*h

• Area of circle

Suppose a circle with its radius r, then the area of circle= π*r^2 

• Area of rhombus

Suppose a rhombus with its diagonals be d1 and d2, then the area of rhombus= ½*d1*d2

• Area of a parallelogram

Suppose a parallelogram with its base b and height h, then the area of parallelogram= b*h

Perimeter

In a closed figure the length of its boundary that is, the sum of its sides is known as the perimeter of that closed figure. In simple language, the length of the boundary of a closed figure is the perimeter of that closed figure. The length of the outline of any closed figure is the perimeter. 

Perimeter is measured in centimeter, meter, kilometer, inched, foot, yard, etc. There is no as such SI unit for perimeter, international standard unit. Perimeter is generally measured in centimeters and meters. 

The formula for finding the perimeter of various 2-dimensional shapes

• The perimeter of a square 

Suppose there is a square with side s, then the perimeter of square= s*4

• The perimeter of a rectangle 

Suppose a rectangle with its length be l and breath be b, then the area of rectangle= 2(l+b)

• Perimeter of triangle

suppose a triangle with its side a, b, c respectively, then the perimeter of triangle= a+b+c

• Perimeter of circle

The perimeter of a circle is generally known as the circumference of the circle. Suppose a circle with its radius r, then the circumference of circle= 2πr

• Perimeter of rhombus

Suppose a rhombus with its side s, then the perimeter of rhombus 4*s 

• The perimeter of a parallelogram

Suppose a parallelogram with its base b and height h, then the perimeter of parallelogram= 2*(b+h)

• The perimeter of an equilateral polygon

Suppose an Equilateral polygon number of side n and side s, then the perimeter of equilateral polygon= n*s 

Difference between area and perimeter

• The unit of the region occupied by a two-dimensional closed figure or shape is called the area of the closed figure whereas, In a closed figure the length of its boundary that is, the sum of its sides is known as the perimeter of that closed figure
• The area is always measured in square units whereas, the perimeter is measured in units
• The SI unit of area is square meters, whereas the perimeter has no SI unit
• Square centimeter, square meter, square feet, square kilometer are measuring units for an area whereas, centimeter, meter, kilometer, feet, yard are the measuring units for the perimeter
• The area of a residential house is an example of an area whereas,  The length of the fence of the same residential house will be an example of perimeter 
• Area of a rectangle= l*b whereas, Perimeter of the same rectangle= 2(l+b)
• Area of square= s*s whereas, the perimeter of the same square=4*s

Let’s understand the difference between area and perimeter with an example

Q: A rectangular house has a length=20m and breath=15m. Find the area of the house and its perimeter.

Length=20 m

Breath=15 m

• Area covered by house= l*b

Therefore, 20*15

= 300 sq.m 

• Perimeter of the house= 2*(l+b)

Therefore, 2*(20+15)

= 70 m

Conclusion

An area is a unit of the region occupied by a two-dimensional closed figure or shape and the perimeter is the distance or length of the outline of a closed figure. Area and perimeter are two different properties of 2-dimensional shapes and figures and have various use in our day-to-day lives. Area and perimeter are two aspects that are studied under mensuration along with other properties such as volume, curve surface area, etc.