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Rectangle Formula
In mathematics, three major formulas are used in solving sums with rectangles. They are, the perimeter of a square, area of a square as well as the diagonal length of a square.
Introduction
The formulae for the diagonal, perimeter as well as the area of a rectangular shape are all included in the formulas of a rectangle.
To refresh your memory, a rectangle shape is a four-sided geometry with an equal extent of opposing sides. Because all of a rectangle’s corners are right-angled. A rectangle can be said as a parallelogram that contains right-angle corners. Moreover, when all the sides of a rectangle are equal then the shape is said to be a square.
In this article let us discuss the formulas of a rectangle which are as mentioned above, the area, perimeter and diagonal.
Area of a Rectangle
As we all know, area is the region enclosed in a particular shape. Here in this case inside a rectangle. Therefore, to find out the area of a rectangle the formula used is,
Area=lb
Where,
l = length of the rectangle
b = rectangle’s breadth or width.
Perimeter of a Rectangle
As well all know that a perimeter is simply the sum of all sides of a rectangle thus mathematically it is shown as,
Perimeter =2(l+b)
Where,
l = length of the rectangle
And b = rectangle’s breadth or width.
Diagonal of a Rectangle
A diagonal is a line that goes from one vertex of a rectangle to its opposite vertex. And the formula used to find the length of a diagonal of a rectangle is given as,
D (Diagonal)=√l2+b2
Where,
D = Diagonal of the rectangle
l = length of the rectangle
And b = rectangle’s breadth or width.
Example
Let us understand these formulas of area, perimeter and diagonal length of a rectangle with the help of an example.
Consider a rectangular field having a length of 50 meters and a width of 20 meters. A person has to build a building over there and has to report the area that the field covers to the builder. Along with the fencing length needed to be done on the boundary. He is also curious to know what could be the distance from one corner of the field to the opposite corner of that. Find out the details that the person wanted.
The answer to this would be:
Initially to report to the builder the person needed to know the area
First, as we know
l = 50 m
b = 20 m
Therefore,
Area=lb
A=5020=1000 m2
And for fencing the boundary the perimeter of the field will be,
Perimeter =2(l+b)
P=2(50+20)=140 m
And at the end the person wanted to measure the distance between two opposite corners of the field which is called the diagonal. Therefore, the diagonal of the field can be found out using the formula,
D (Diagonal)=√l2+b2
D=√502+202
D=√2500+400
D=√2900
D=10√29 m
As per the question, the area of the rectangular field is 1000 m2, fencing length is 140 m as well as distance from one corner to another corner is 1029 m.
