Evelyn Maitee Marin
Industrial Engineer, MSc in Physics, and EdD
The term quadrilateral, from the Latin quadrilaterus, refers to the fact that “it has four sides”, which is why in Euclidean geometry it is defined as a geometric figure composed of four sides: four internal angles and four vertices. Quadrilaterals, also known as quadrangles or tetragons, have countless applications in almost any area of knowledge, since they are used in designs, civil constructions, representation of chemical bonds, among others.
elements of quadrilaterals
Regardless of the type of quadrilateral, it will always be made up of the following characteristics:
• Four sides, four interior angles, and four vertices.
• Two diagonals that cross the figure from one corner to another and divide the quadrilateral into four triangles.
• The internal region bounded by its four sides forms an area.
The figure indicates the constituent elements of the quadrilaterals
Classification of quadrilaterals
Scheme showing the classification of quadrilaterals according to the arrangement of their sides.
Quadrilaterals can be divided into three categories, which in turn can be subdivided into other categories, whose characteristics are described below:
• Parallelograms: they are so called because they have two pairs of parallel sides. They are classified in:
o Square: this figure has its four sides of equal length and its four internal angles are right (90°). Squares have lines of symmetry that are horizontal, vertical, and their diagonals.
The dashed lines represent the axes of symmetry of the square, and the point of intersection of these lines represents its geometric center or centroid of area.
o Rectangle: this quadrilateral is characterized by having two pairs of sides of equal length. Adjoining sides are unequal and, like squares, have four internal angles of 90°.
Many everyday objects have a rectangular shape, such as the pages of notebooks, the screen and keyboard of a laptop or the screen of a cell phone.
Rhombus: like the squares, this quadrilateral has its four sides with the same length parallel two to two, but their opposite internal angles are equal, two acute (less than 90°) and two obtuse (greater than 90°).
This traffic signal indicates that vehicles circulate in both directions and its outline is formed by a rhombus.
Rhomboid: has opposite sides and angles equal two to two. Their adjacent sides are different. Like the rhombuses, they have two acute (less than 90°) and two obtuse (greater than 90°).
This symmetrical six-pointed star is formed by the arrangement of six rhomboids that touch at one of their vertices.
• Trapezoids: these shapes have two sides parallel to each other but with different lengths, and two non-parallel sides. The parallel sides are called the major base and the minor base based on their dimensions. The trapezoids are classified in turn into:
o Rectangle trapezoid: this trapezoid owes its name to two of its internal angles being right (equal to 90°). The other angles are one acute (< 90°) and the other obtuse (> 90°).
The trapezoid in the image is of the rectangle type. Two 90° internal angles and two parallel opposite sides called base are observed, in this case, the smaller base is the upper side and the larger is the lower side.
o Isosceles trapezoid: this trapezoid has an axis of symmetry, since its two non-parallel sides have the same measure.
The isosceles trapezoid shown has its lateral sides with the same length, its axis of symmetry is the segmented vertical line.
o Scalene trapezoid: this trapezoid does not have symmetry, since none of its sides have the same length. In addition, it differs from the right trapezoid because none of its angles are right.
The adjective scalene is used in geometric figures to express that all the sides are unequal, as in the case of the scalene trapezoid shown.
Trapezoids: these figures do not have a sub-classification, and those quadrilaterals that do not have equal sides or angles are grouped here.
The outline of the kite, kite or parrot has a trapezoid shape, since neither its sides nor its internal angles are equal.
Areas and perimeters of quadrilaterals
In boxing and other combat sports, the cordoned off area where the fight takes place is called a ring because it is a closed region bounded by four sides.
Perimeter: In all figures, the perimeter is determined by the sum of its sides. If each of the sides of a quadrilateral is called l1, l2, l3 and l4, its perimeter (P) is determined by the expression:
\(P = {l_1} + {l_2} + {l_3} + {l_4}\)
The units of the perimeter must correspond to the length dimension, for example, meters (m), centimeters (cm), inches (in), etc.
Area: In the case of the areas of squares and rectangles, it is determined by multiplying the base (b) by the height (h):
\(A = b \cdot h\)
For trapezoids, the area is determined by half the sum of their bases multiplied by their height:
\(A = \left( {\frac{{b + B}}{2}} \right) \cdot h\)
In the case of rhombuses and rhomboids, the area is found by multiplying their diagonals divided by two:
\(A = \frac{{D \cdot d}}{2}\)
In trapezoids, the area must be determined by dividing it into other, simpler figures, for example, into two triangles. The area of each of the figures that compose it is determined and then added:
\(A = \sum {A_i}\)
Note: The dimension of an area must be length squared, for example, meters squared (m2).
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