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A quadrilateral with equal angles and parallel opposite sides is referred to as a rectangle. Around us, there are a lot of rectangle items. The length and width of any rectangle form serve as its two distinguishing attributes. The width and length of a rectangle, respectively, are its longer and shorter sides. The attributes of the rectangle shape will be covered in this article.
Describe the rectangle:
A rectangle is a closed, four-sided figure in two dimensions. All of a rectangle’s angles are equal to 90 degrees, and its opposite sides are equal and parallel to one another. See the shape, sides, and angles of the rectangle in the illustration below.
Rectangle’s Properties:
A closed figure with four sides that forms a 90° angle is known as a rectangle. A rectangle can have many different characteristics. The following list includes some of a rectangle’s key characteristics.
A quadrilateral is a rectangle
A rectangle’s opposing sides are equal and parallel to one another
Each vertex of a rectangle has a 90° internal angle
360° is the total of all interior angles
The diagonals cut each other in half
The diagonals are all the same length
The Pythagorean theorem can be used to determine the length of the diagonals.
Diagonal = (a2 + b2) is the formula for the measurement of a diagonal with sides a and b
A rectangle is also referred to as a parallelogram since its sides are parallel
While all parallelograms are rectangles, not all rectangles are parallelograms
A rectangle’s diagonal:
A line segment that connects any two of a rectangle’s non-adjacent vertices is said to be its diagonal. The diagonals that are of equal length in the rectangle below are AC and BD.
A diagonal divides a rectangle into two right-angled triangles; the diagonal serves as the hypotenuse of the triangle, while the two neighbouring sides of the rectangle serve as its other two sides.
Rectangle’s diagonal formula:
The formula for the diagonal of a rectangle is obtained using the Pythagoras theorem. 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 diagonal (d): √(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).
Rectangle’s surface area:
The quantity of unit squares that can fit inside a rectangle called its area. In other terms, the area of a rectangle is the area that it occupys. The flat surfaces of laptop monitors, blackboards, painting canvases, etc. are a few instances of rectangular shapes. To determine the area that these objects occupy, we can utilize the rectangle’s area formula.
Formula for Area of Rectangle:
The product of a rectangle’s length and width, or “l” and “w,” gives the area of the rectangle, which is expressed as follows:
Rectangular Area = (l x w)
Circumference of a Rectangle:
The length of a rectangle’s entire boundary is known as its perimeter. It is given in linear measures like cm, inches, and so on and can be interpreted as the entire measurement of the rectangle’s length and width. For instance, if you need to adorn the border of your rectangular notebook, you can quickly determine how much ribbon you’d need by calculating the perimeter. Similarly, if you need to build a fence around your garden, calculating the perimeter will tell you exactly how much wire you’d need. Below is a description of the formula used to determine a rectangle’s perimeter.
Rectangle’s perimeter 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).
Conclusion
In a rectangle, the opposing sides are equal and parallel. The diagonals of a rectangle are equal and cross each other. They cross each other in the middle, which is referred to as being bisected. Angles that follow each other in a rectangle are supplementary.
They are 180 degrees in total. If a rectangle has a height of h and a base of b, then the area it corresponds to is determined by multiplying b by h.The opposing sides of a rectangle are equal to one another.
