What is Perimeter and Area in Math?
A perimeter is a route that encompasses/surrounds/outlines a form in two dimensions, or it is its length (one-dimensional). The circumference of a circle or an ellipse is its perimeter.
There are numerous practical applications for calculating the perimeter. A measured perimeter is the length of fencing needed to completely encircle a yard or garden. The perimeter (circumference) of a wheel/circle specifies how far it will roll in one revolution. Likewise, the quantity of thread wrapped around a spool is proportional to the spool’s perimeter; if the string length were precise, it would match the perimeter.
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The perimeter as well as area of geometric shapes are the two most important measurements. A typical mistake is to mix them together, as well as to believe that the greater one is, the greater the other must be. Indeed, it is a well-known fact that enlarging (or contracting) a form increases (or decreases) its area as well as its perimeter. The real field perimeter can be determined by multiplying the drawing perimeter by 10,000, for instance, if a field is depicted on a 1/10,000 scale map. The true area of the shape on the map is 1,00,002 times that of the shape on the map. However, there is no relationship between an ordinary shape’s area and its perimeter.
The area of a two-dimensional region, form, or planar lamina in the plane is the quantity that represents its extent. On the 2D surface of a three-dimensional object, surface area is its counterpart. Area can be defined as the amount of material with a specific thickness necessary to construct a model of the design or even the amount of paint required to cover the region in a single coat. It is the 2D equivalent of the length of a curve or even the volume of a solid. A shape’s area can be calculated by comparing it to squares of a specific size. The standard unit of area in the International System of Units (SI) is the square meter (represented as m2), which is the area of a square with sides that are one meter long. A three-square-meter form has the same area as three squares of the same size. The area of the unit square is one, while the area of any other shape or surface is a dimensionless real number in math.
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The area of a solid shape’s boundary surface, such as a sphere, cone, or cylinder, is referred to as the surface area. The ancient Greeks had formulas for computing the surface areas of basic forms, but determining the surface area of a more sophisticated shape typically necessitates multivariable calculus.
In modern mathematics, area is very significant. Area is linked to the determination of determinants in linear algebra and is a basic characteristic of surfaces in applied mathematics, in addition to its apparent relevance in geometry as well as calculus. The area of a subset of the plane is determined using the Lebesgue measure in analysis, however not all subsets are measurable.
Application of area and perimeter in daily life
Area and perimeter have several applications in our daily lives. We may see a variety of rectangular parks, square plots, triangular fields, and so on, all of which have areas and perimeters. Formulas can be used to determine these characteristics.
The applications of area and perimeter can identify not only the area and perimeter of a field, but also the area and perimeter of cross pathways or foot routes that surround the field. In this post, we’ll look at some instances of how the area and perimeter formulae for various shapes are used.
Problem 1: If the rectangular field’s length is 40 meters and its width is 20 meters, calculate the total distance around it. Determine the field’s size as well.
Solution: Given,
Length of the field = 40 meters
Width of the field = 20 meters
We can calculate the total distance around a rectangular field using the perimeter formula,
Perimeter = 2 (Length + Width)
= 2 (40 + 20) meters
= 2 x 60 meters
= 120 meters
Area of the field (Rectangle shape) = Length x width
= 40 x 20 meter2
= 800 meter2
Therefore, total distance around it is 120 meter and the size of the field is 800 m2.
Problem 2: If the rectangular field’s length is 60 meters and its width is 20 meters, calculate the total distance around it. Determine the field’s size as well.
Solution: Given,
Length of the field = 60 meters
Width of the field = 20 meters
Now, we can calculate the total distance around a rectangular field using the perimeter formula,
Perimeter = 2 (Length + Width)
= 2 (60 + 20) meters
= 2 x 80 meters
= 160 meters
Area of the field (Rectangle shape) = Length x width
= 60 x 20 meter2
= 1200 meter2
Therefore, total distance around it is 160 meter and the size of the field is 1200 m2
Attempt this question: A rectangular park is 45 m long and 30 m wide. A path 2.5 m wide is constructed outside the park. Find the area of the path?
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