defination of rectangular track
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Explanation:
A rectangle
A rectangle is a type of quadrilateral. In fact, it is also called equiangular quadrilateral as all the angles are equal. There are many rectangular objects around you. Each rectangular shape is characterized by two dimensions, its length, and width. The longer side of the rectangle we call is the length and the shorter side is called width. In this chapter, we will learn about rectangle shape and its properties.
What is a Rectangle?
A rectangle is a closed two-dimensional figure with four sides and four corners. The length of the opposite sides is equal and parallel to each other. The adjacent sides of a rectangle are meet at the right angle that is, the angle formed by the adjacent sides of a rectangle is 90°. The basic feature of a rectangle is given below.Diagonal of a Rectangle
The diagonal of a rectangle is a line segment that joins any two of its non-adjacent vertices. In the following rectangle, AC and BD are the diagonals. You can see that the lengths of both AC and BD are the same. A diagonal cuts a rectangle into 2 right triangles, in which the sides equal to the sides of the rectangle and with a hypotenuse. That hypotenuse is the diagonal.
Diagonal of a rectangle
Diagonal of Rectangle Formula
The formula for the diagonal of a rectangle is derived using the Pythagoras theorem. The length of the diagonal of the Rectangle is found using the formula shown below. Let us consider a rectangle of length "l" and width "w". Let the length of each diagonal be "d". Applying Pythagoras theorem to the triangle ABD, d2 = l2 + w2. Taking square root on both sides, √(d2) = √( l2 + w2). Thus, the diagonal of a rectangle formula is: √(l² + w²) and thus the diagonals of a rectangle can be calculated when the length and width of the rectangle are known.
Diagonal of Rectangle (d) = √(l² + w²)
Area of a Rectangle
The area of a rectangle is the number of unit squares that can fit into a rectangle. Some examples of rectangular shapes are the flat surfaces of laptop monitors, blackboards, painting canvas, etc. You can use the formula of the area of a rectangle to find the space occupied by these objects. For example, let us consider a rectangle of length 4 inches and width 3 inches. Let us draw unit squares inside the rectangle. Each unit square is a square of length 1 inch. Now, count the number of unit squares in the above figure. How many squares can you observe? There are 12 squares in total. We have already learned that area is measured in square units. Since the unit of this rectangle is "inches," the area is measured and written in square inches. Thus, the Area of the above rectangle = 12 square inches. Thus, the area of a rectangle can be calculated when its sides(length and breadth) are known.
The area of a rectangle is the number of unit squares that can fit into a rectangle.
Area of Rectangle Formula
The formula for the area, 'A' of a rectangle whose length and width are 'l' and 'w' respectively is the product "l × w".
Area of a Rectangle = (Length × Width) square units
Perimeter of a Rectangle
The perimeter of a rectangle is the length of the outer boundary of a rectangle. It can be taken as the sum of the total measure of the length and breadth of the rectangle. The perimeter of a rectangle helps us in calculating distances and lengths in our day-to-day lives. For example, if you need to decorate the border of your rectangular notebook, you can easily calculate how much ribbon you would need by finding the perimeter or if you need to put a fence around your garden, the perimeter of the garden will give you the exact length of wire you would need. The formula used to calculate the perimeter of a rectangle is:
Perimeter of Rectangle Formula
The formula for the perimeter, 'P' of a rectangle whose length and width are 'l' and 'w' respectively is 2(l + w).
Perimeter of a Rectangle Formula = 2 (Length + Width) units
Properties of a Rectangle
A rectangle is a closed figure of four sides having two equal pairs of opposite sides and the angle formed by adjacent sides is 90 degrees. A rectangle can have a wide range of properties. Some of the important properties of a rectangle are given below.
A rectangle is a quadrilateral.
The opposite sides of a rectangle are equal and parallel to each other.
The interior angle of a rectangle at each vertex is 90°.
The sum of all interior angles is 360°.
The diagonals bisect each other.
The length of the diagonals is equal.
The length of the diagonals can be obtained using the Pythagorean theorem. The length of the diagonal with sides a and b is √( a2 + b2).
Since the sides of a rectangle are parallel, it is also called a parallelogram.
All rectangles are parallelograms but all parallelograms are not rectangles.
If two diagonals bisect each other at 90°, it forms a square.
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