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In mathematics, the two most essential features of two-dimensional forms are their area and perimeter. The perimeter of a shape indicates the distance between its boundaries, whereas the area of a shape describes the area occupied by the shape. Area and perimeter are significant topics in mathematics that are applied in many aspects of our daily lives. This is relevant to any shape and size, regardless of whether they are regular or irregular. Every shape has its own formula for calculating its area and perimeter.
Area
The area of an object is the region that is defined by the shape of the object. The area of a figure or any two-dimensional geometric shape is the space covered by the figure or shape in a plane that is defined by the figure. The area of all the shapes is determined by the dimensions and attributes of the shapes. Different forms have a variety of surface areas. The area of a square differs from the area of a kite in terms of size.
If two things have a similar shape, it is not necessary that the area covered by them be the same unless and until the dimensions of both objects are the same as well. Consider the following scenario: there are two rectangle boxes with lengths L1 and L2 and widths B1 and B2. As a result, the areas of both rectangular boxes, say A1 and A2, will be equal only if L1=L2 and B1=B2; otherwise, they would be unequal.
Perimeter
Perimeter is defined as the complete distance around a shape and is measured in metres. Essentially, the perimeter of any shape is the length of the shape when it is enlarged in a linear fashion. In a two-dimensional plane, a perimeter is the total distance that encircles a shape. It is possible for the perimeters of distinct forms to be the same length as each other depending on their size.
For example, if a circle is constructed from a metal wire of length L, the same wire can be used to make a square with sides that are all of the same length.
Differences between area and perimeter
The following is a list of the distinctions between area and perimeter:
Area | Perimeter |
The region occupied by a form is referred to as its area. | The perimeter of a shape is the total distance covered by the shape’s boundaries. |
The area is measured in square units (m2, cm2, in2, etc.) | The length of a perimeter is measured in units of length (m, cm, in, feet, etc.) |
A rectangular ground’s surface area is equal to the product of its length and width. | A rectangular ground has a perimeter equal to the total of its four boundaries, which is equal to 2(length + breadth). |
Area and perimeter for all shapes
There are numerous shapes to choose from. The most frequently encountered shapes include the square, triangle, rectangle, circle, and so on. Different formulas are required to determine the area and perimeter of each of these objects.
Area and perimeter of a rectangle
A rectangle is a figure or shape with opposite sides that are the same length and all angles that are the same angle. In an XY plane, the area of a rectangle is the space that it occupies on the diagonal.
Perimeter of a rectangle = 2(a+b)
Area of a rectangle = a x b
In which a and b denote the length and width of the rectangle, respectively.
Perimeter and area of a square
A square is a figure or form that has equal lengths on all four sides and angles that are all 90 degrees. Area of the square is the space occupied by the square in 2D plane, while perimeter of the square is the distance covered by the square on the outside line.
Perimeter of a square = 4a
Area of a square = a2
the length of one of the square’s sides is denoted by the letter a.
Perimeter and area of a triangle
The triangle is made up of three sides. The perimeter of any given triangle, regardless of whether it is a scalene, isosceles, or equilateral, will be equal to the total of the lengths of all three sides in each particular case. In addition, the area of each triangle is the space filled by it in a plane, as seen in the figure.
Perimeter of a triangle = a + b +c , where a, b and c are the three different sides of the triangle.
Area of a triangle = ½ b × h; where b is the base and h is the height of the triangle.
Area and circumference of a circle
The region occupied by a circle in a plane is referred to as its area.
In the case of a circle, the distance of the outer line of the circle is called the circumference.
Circumference of Circle = 2πr
Area of Circle = πr2
Where r is the radius
Applications of area and perimeter
We already know that the area of these shapes is essentially the space covered by them, and that the perimeter of the shapes is the distance around them. You need to know the area of your new home before you can determine the amount of paint you’ll need and how much it’ll cost to paint the walls.
For example, if you want to fence in your garden at home, the length of fencing material you’ll need is equal to the length of the garden’s perimeter. The perimeter of a square garden with each side measured in centimetres would be 4 centimetres. The area of a shape or a specified figure is the volume of space contained within the shape or figure. It is expressed as a number of square units.
Conclusion
The area of a shape is a measure of how much space there is within it. Knowing the area of a shape or surface is useful in everyday life; for example, you may need to know how much paint to purchase in order to cover an unsightly wall or how much grass seed to sow in order to properly maintain a lawn.
