Evelyn Maitee Marin
Industrial Engineer, MSc in Physics, and EdD
A rectangle is a flat geometric configuration whose shape is characterized by having four right angles (of 90 degrees, which internally total 360 degrees) determined from its four sides, where the respective opposites are parallel and congruent to each other. It is a special type of parallelogram. by the latin rectanglelusis constituted on rectus, of rectum, and angŭlusbased on the Greek form ἀγκύλος (ankylos), as an adjective that describes something ‘arched’, ’tilted’, ‘curved’. It is distinguished as a very common shape in geometry and in everyday life, and is used in the construction of buildings, the manufacture of furniture, in the creation of topographic plans, etc.
For example, the pool table forms a rectangle, the standard dimensions of which are 188 cm x 96 cm for the playing area.
Characteristics and properties
• It has four sides that are two-to-two congruent, that is, opposite sides have the same length.
• It has four right angles, which means that each angle measures 90 degrees.
• It has two diagonals that are congruent and intersect at the center of the rectangle.
• Its opposite sides are parallel.
Regarding lines of symmetry, a rectangle has two lines of symmetry, each of which divides the rectangle into two equal halves. The axes of symmetry pass through the center of the rectangle and are perpendicular to each other. In a rectangle, the geometric center is found at the point of intersection of the diagonals.
Rectangles are quadrilaterals with four congruent sides, two by two, and four right angles. They have two axes of symmetry that intersect at their geometric center. In the hollow cross section of the block, the axes of symmetry of said section can be seen.
How is the diagonal determined in a rectangle?
To determine the diagonal of a rectangle, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In the case of the rectangle, the other two sides are the base and the height.
Therefore, to calculate the diagonal of a rectangle with base b and height h, one can do the following:
Find the length of one of the sides of the right triangle formed by the diagonal, the base and the height. In this case, you can choose either the base or the height as one of the sides of the triangle. For example, if height is chosen, the length of the side will be h.
Find the length of the other side of the right triangle. In this case, it will be the base. Therefore, the length of the other side will be b.
Use the Pythagorean theorem to find the length of the hypotenuse, which will be the diagonal of the rectangle. So, the diagonal (D) can be calculated as:
\(D = \sqrt {{b^2} + {h^2}} \)
For example, if the rectangle has a base of 6 cm and a height of 8 cm, the diagonal can be calculated as:
\(D = \sqrt {{6^2} + {8^2}} \)
\(D = \sqrt {36 + 64} = \sqrt {100} = 10\;cm\)
Therefore, the diagonal of this rectangle is 10 cm.
At a commercial level, the dimensions of a monitor in inches refer to the measurement of its diagonal; Thus, if a television is 42”, this implies the measurement of its diagonal, drawing a line that crosses from the upper left (or right) end to the lower right (or left).
area and perimeter
To calculate the area and perimeter of a rectangle, you can use the following formulas:
Area = base x height
Perimeter = 2 x (base + height)
where the base and the height are the lengths of the sides of the rectangle.
For example, suppose we have a rectangle with a base of 7 cm and a height of 5 cm. To calculate the area, do the following:
Area = base x height
Area = 7 cm x 5 cm Area = 35 cm²
To calculate the perimeter, do the following:
Perimeter = 2 x (base + height)
Perimeter = 2 x (7 cm + 5 cm)
Perimeter = 2 x 12 cm
perimeter = 24cm
Therefore, the area of this rectangle is 35 cm² and its perimeter is 24 cm.
Examples of practical application
The rectangle is one of the simplest geometric figures and at the same time appreciated by engineers and architects, due to its great aesthetic value and symmetry.
• Frames and pictures: Many pictures and frames are rectangular in shape, making them easy to frame and hang on the walls.
• Electronic displays and televisions: Most electronic displays, including televisions, are rectangular in shape.
• Construction: The bricks and blocks used in the construction are mostly rectangular, which greatly facilitates the construction process.
• Windows and doors: Many windows and doors are rectangular in shape, allowing them to fit properly into wall openings.
• Boxes and packages: Many boxes and packages come in a rectangular or square shape, making them easy to stack and transport.
• Land and Lots: Rectangle-shaped properties are very common in urban planning and land subdivision.
• Books and notebooks: Most books and notebooks are rectangular in shape, making them easy to stack and store.
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