Rectangle – What is it, definition and concept

The rectangle is a quadrilateral, specifically a parallelogram, that has two pairs of sides of equal length. In turn, all interior angles are right, that is, they measure 90º.

That is, the rectangle is a quadrilateral with two pairs of sides that measure the same and that, at the same time, are parallel to each other (they do not cross, although they are prolonged).

As we already mentioned, the rectangle is a category of parallelogram. This is a type of quadrilateral where opposite sides are parallel to each other. However, not all parallelograms have the same characteristics.

Another case of parallelogram is, for example, the rhombus, where all the sides have the same length. However, only two pairs of angles are congruent (they measure the same). On the other hand, in the case of the rectangle, its four angles are equal.

Another characteristic of the rectangle is that its two diagonals are not of equal measure.

Rectangle elements

The elements of the rectangle, as we can see in the following graphic, are the following:

  • Vertices: A, B, C, D.
  • Sides: AB, BC, DC, AD. Where AB = DC and AD = BC
  • Diagonals: AC, DB.
  • Interior angles: They are all straight (they measure 90º).
Rectangle

Perimeter, diagonal and area of ​​the rectangle

The formulas to know the characteristics of the square are the following:

  • Perimeter (P): It is the sum of the four sides. Guiding us from the figure above, it would be: P = 2a + 2b
  • Diagonal: We must remember that the diagonals divide the rectangle into two equal triangles that are right triangles, that is, they are formed by a 90º right angle and two angles smaller than 90º. The right angle is constituted by the union of two sides called legs. Meanwhile, the side of the triangle that is opposite the right angle is called the hypotenuse. So, if we take, looking at the figure above, the triangle formed by the vertices A, B and D, the hypotenuse would be the side DB, while the legs are AB and AD.

The Pythagorean theorem tells us that if we square the legs and add them, we will obtain the hypotenuse squared, as we see in the following formula (where d is the length of the diagonal, a is the length of AB and b is the length of AD.

Diagonal Rectangle
  • Area (A): The area is calculated by multiplying the base by the height, which in the case of the rectangle would be the two sides that do not measure the same and are contiguous: A = axb

Rectangle example

Suppose we have a rectangle with one side that is 20 meters and the other is 16 meters. We can then find:

Perimeter: P = (2 * 20) + (2 * 16) = 72 meters

Diagonal:

Diagonal Rectangle

Area: A = 20 * 16 = 320m2

Now let’s look at another example. Suppose we are given as data that one of the sides of the rectangle is 12 meters and that the diagonal is 30.5 meters. What would be the perimeter and area of ​​the figure?

In this case, we would have to use the Pythagorean theorem, taking into account that the diagonal is the hypotenuse and the sides of the rectangle are the legs:

d2 = a2 + b2

30.52 = 122 + b2

930.25 = 144 + b2

b2 = 786.25

b = 28.0401 meters

So, we can calculate the perimeter and the area of ​​the rectangle:

P = (12 x 2) + (28.0401 x 2) = 80.0803 meters

A = 12 x 28.0401 = 336.4818 m2

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