Properties Of A Rectangle

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What Are The Properties Of A Rectangle

Mathematics students always ask What Are The Characteristics Of A Rectangle or rather What Are The Properties Of A Rectangle in geometry? By way of definition one can say that a rectangle is a 2 dimensional plane figure which has 4 sides. Thus we can describe a rectangle further as a polygon with four sides. However, take good note that the opposite sides of a rectangle are parallel to each other as well as equal to each other. A rectangle remains one of the forms of a quadrilateral whose four interior angles are equal to 90 degree or are right angle.

Meanwhile, a rectangle can also be taken to be a very special type of parallelogram whose 4 angles are equal to each other. Any rectangle in which the four sides are equal can be referred to as a square. Having known in brief terms what a rectangle is, we need to go forward to enumerate further the properties of a typical rectangle.

Properties Of A Rectangle Geometry

Rectangle Properties – Basically, the fundamental 4 properties of a rectangle for kids and many more includes the following:

A rectangle is a type of quadrilateral because it is a plain figure bearing four sides.

The opposite sides of a rectangle are not only equal to each other rather, they are also parallel to each other.

Each of the interior angles found in a rectangle is a right angle because they are each equal to 90 degrees.

The sum of all the 4 interior angles of a rectangle is equal to 360 degrees.

The diagonals of a rectangle bisect each other.

The 2 diagonals found in a rectangle are equal in length.

The perimeter of a typical rectangle with side lengths c and d can be calculated as 2c+2d units.

The area of a typical rectangle with side lengths c and d can be computed correctly as cd sin 90 = cd square units.

The diagonal of any given rectangle is the same size as the diameter of its circumcircle.

If c and d are given as the sides of a rectangle, you can calculate the length of each diagonal (d) as d² = c² + d²

The diagonals of a rectangle bisect each other at varying angles. While one of the angles is an obtuse angle, the other angle is an acute angle.

A rectangle can be considered to be a square if the the angles where its two diagonals bisect each other is 90 degrees (that is right angles).

If a rectangle is rotated along the line joining the midpoint of its longer parallel sides, a cylinder is formed. In such a case, width of the rectangle will be equal to the height of the cylinder. Also, the length of a rectangle also becomes equal to the diameter of the cylinder.

If you rotate a rectangle along the line joining the midpoint of the shorter parallel sides, you will get a cylindrical figure. In such a scenario, the length of a rectangle becomes equal to the height of the cylinder while the width of the rectangle become equal to the diameter of the cylinder obtained.

Example: If the length of a rectangle is 20 cm and the width is 15 cm, compute the perimeter of the rectangle.

Solution: Perimeter Of Rectangle = 2 (Length + Width)

From the question above, we were given that the rectangle’s length is 20 cm while its width is 15 cm.

Thus Perimeter Of Rectangle = 2 x (20 + 15)

Perimeter Of Rectangle = 2 x 35

Therefore, Perimeter Of Rectangle = 70 cm

What Are The 5 Properties Of A Rectangle

The 5 properties of a rectangle includes the following:

1. A rectangle is a quadrilateral shape. It has four defined sides.
2. The opposite sides of a rectangle are equal to each other and also, they are parallel to each other.
3. The value of each interior angle found in a rectangle is equal to 90 degrees (a right angle).
4. When you add together the values of all the interior angles of a rectangle, your answer will be equivalent to 360 degrees.
5. The diagonals of a rectangle are equal in length and they bisect each other.

State The Properties Of A Rectangle

The fundamental definition of a rectangle has it that it is a parallelogram bearing four right angles. Alternatively, we can also describe a rectangle as a quadrilateral whose four interior angles are each equal to 90 degree. That is to say that each of the interior angles of a rectangle is a right angle. The characteristics of a rectangle in geometry are as follows:

• A rectangle has 4 interior angles each of which is valued at 90°. They are all right angles. As such, all rectangles can be considered to be parallelograms because of the fact that the opposite interior angles of a rectangle are equal to each other.
• The diagonals of any rectangle bisect each other.
• The opposite sides of a rectangle are parallel to each other.
• Also, the opposite sides of a rectangle are equal to each other.
• The area of a rectangle with side lengths x and y can be computed as ab sin 90° = ab.
• The perimeter of a rectangle with side lengths x and y can be calculated as 2x + 2y.
• The length of each diagonal of a rectangle whose side lengths are x and y is √x² + y².
• The lengths of the two diagonals of a rectangle are equal.
• If O is the points where the 2 equal length diagonals of a rectangle bisect each other then, each vertex of a rectangle must be equidistant from that point of bisection O. Thus, it goes further to assert that there exists a circumcircle through O which moves through the four vertices of the rectangle.
• With O still remaining the point of where the diagonals of a rectangle intersects each other, it also follows that there exists a circumcircle centered at O whose radius is equal to half of the length of the rectangle’s diagonal.
• Each diagonal of a rectangle is a diameter of the circumcircle of the same rectangle.

What Are The Properties Of A Rectangle In Geometry

What is Rectangle? – A rectangle can be defined as two-dimensional plane figure made up of four sides. It follows that rectangle is a four-sided polygon whose opposite sides which are of the same length are parallel to each other.

Thus, a rectangle is one of the forms of a quadrilateral bearing 4 angles each of which is equal to 90 degrees (that is right angles). Also, a rectangle also qualifies as a parallelogram with equal angles. If a rectangle have the four sides equal to each other, it will be referred to as a square. Thus, all rectangles cannot be a square but a square is a rectangle. A Kite is also a form of rectangle.

List All The Properties Of A Rectangle

The length (l) and the width of any rectangle defines its shape and size. A rectangle WXYZ has 4 sides WX, XZ, WY, and YZ. In the same vein, the 4 right angles of this given rectangle can be labelled W, X, Y and Z respectively.

The length (L) of the distance between point W and point X or the distance between points Y and Z can be called the length (L) of this particular rectangle. On the other hand, the width (W) of this rectangle can also be described as the shortest distance between points W and Y as well as points X and Z.

Shape Of Rectangle

As already stated earlier, a rectangle is a two dimensional (2D) plane figure with four sides. We can easily represent a rectangle in an XY plane by using the arms of the x-axis and the y-axis to indicate the length and width of the rectangle, respectively.

Types Of Rectangle

There are two major types of rectangle which we are going to outline and throw more light on in this section. Recall, that a geometric figure bearing four sides and four right angles perfectly defines a rectangle in simple terms. Explaining further, we can agree more together that besides the opposite sides of a rectangle being equal to each other, the opposite sides are also parallel to each other while the adjacent sides of a rectangle meet each other at an angle of right angles measuring 90°. With this insight on the characteristics of a rectangle, we will go forward to discus the types of rectangles below:

1. A Square: One of the distinguishing feature of a square is that it is a perfectly symmetrical geometric figure. A Square can be defined as a type of rectangle which has four equal angles as well as four equal sides. Looking at the square shape from a two dimensional view, we can deduce that each of the interior angles formed at each of the four vertices of a square is equal to 90° (a right angle). As seen in a typical rectangle, the opposite sides of a square are parallel to each other as well as equal in length to each other. Adding to these insights so far, it is also worthy to note that the diagonals of a square bisect each other at 90 degrees. In conclusion, we can agree that all rectangles are not squares but all squares are rectangles.
2. Golden Rectangle: The golden rectangle can be referred to as a perfect plane rectangular shape bearing sides which are in the golden ratio form. To refresh your memory, recall that a golden ratio can be defined in mathematical terms as a condition where (x + y)/x = x/y, where ‘x’ represents the breadth of the figure in question and (x + y) stands for the length of the rectangular figure. Thus, we are in the right direction if we assert that the golden rectangle describes any rectangle where the ratio of its length to its width is in the golden ratio of 1 : (1 + √5/2). Thus, the Golden Ratio is always approximately to 1 : 1.618.

Rectangular Shape Objects

In our day to day lives, we come across several rectangular shape images, rectangular shape things, rectangular shape sign, rectangular shape 3D and the likes of the. Some of them includes computer screens, Televisions, cell phones, notebooks, notice boards, CPUs, books, tables, mobile phones, TV screens, magazines, walls, tennis courts and many others.

Properties of A Square In Geometry

The characteristics of a square in the context of mathematical geometry includes the following:

1. Each of the four interior angles of a square is equivalent to 90° degrees.
2. The four sides of a square are congruent. That means that they are equal to one another.
3. The opposite sides of a square are parallel to each other.
4. The square diagonals of a square bisect each other and are 90 degrees away from each other.
5. The 2 diagonals of a square have the same length measurements.
6. A square features four vertices and four sides as well.
7. The diagonal of a square diagonal divides the shape into two identical isosceles triangles.
8. The length of each side of a square is lesser than the length of the two diagonals of a square.

Rectangle Properties Geometry

For any typical plane rectangular figure, the following features can be used to give an in-depth description for it for better understanding.

A rectangle has 4 sides hence, it is referred to as a quadrilateral.

Each of the interior angles of a rectangle measures 90 degrees. Also, the opposite sides of a rectangle are same in size and are parallel to each other.

If you add the values of the interior angles of any given rectangle together, you are bound to get a total of 360 degrees.

The diagonals of a rectangle are identical in length and are also parallel.

The perimeter of a rectangle with side lengths x and y can be said to be 2 x+2 y units.

The area of a rectangle with side lengths x and y is xy sin 90 = xy square units.

The diameter of the circumcircle of a rectangle is diagonal.

The length of each diagonal (d) of a rectangle is given as d² = √x² + b² assuming x and y are used to depict the sides of the rectangle.

At different angles, the diagonals of a rectangle bisect each other. One of the angles is an obtuse angle while the other angle is an acute angle.

A rectangle can be called a square if its two diagonals bisect each other at 90° right angles.

A cylinder can be formed from a rectangle if the rectangle is rotated along the line that connects the midpoints of the longer parallel sides. By implication, the height of the cylinder becomes equal to the width of that particular rectangle. Owing to this, the diameter of the formed cylinder also becomes equal to the length of the rectangle.

However, if the rectangle is rotated along the line connecting the midpoints of the shorter parallel sides, a cylinder is also formed as a result. But in this scenario, the height of the cylinder will be identical with the length of the rectangle. In the same vein too, the diameter of the formed cylinder will also be equal to the width of the rectangle.

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