A polygon having four sides, four angles, and four vertices is known as a quadrilateral. When naming a quadrilateral, it’s important to remember the vertices’ order. The following quadrilateral, for example, should be labeled ABCD, BCDA, ADCB, or DCBA. Because they modify the sequence of vertices in which a quadrilateral is constructed, it can’t be called ACBD or DBAC. ABCD is a quadrilateral with four sides (AB, BC, CD, DA), as well as two diagonals (AC and BD).
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Each of the quadrilaterals mentioned above has its unique set of characteristics. There are, nevertheless, some qualities that all quadrilaterals share. The following are the details.
- There are four sides to them.
- They are made up of four vertices.
- They are divided into two diagonals.
- 360° is the total of all interior angles.
We’ll go through the additional features of several quadrilaterals in depth. The qualities of quadrilaterals can be used to identify a quadrilateral.
A square is a type of quadrilateral in which all four sides are equal in length and all four angles are 90°.
When two pairs of parallel sides form congruent adjacent angles, the figure is known as a parallelogram. The opposite sides of a parallelogram are also congruent, allowing for the formation of rectangles, which can come in horizontal or vertical orientations with respect to each other. Sometimes only one pair of parallel sides (usually the top and bottom) will be explicitly stated while identifying a parallelogram. In this case, it’s implied that the second pair is parallel to the first and congruent to them.
A rectangle is a four-right-angled parallelogram. A square is a rectangle and a quadrilateral at the same time.
A rhombus is defined as a parallelogram with all sides of equal length. If two pairs of opposite sides are parallel, the figure is known as an oblong or an oblong rhombus.
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A trapezoid has only one pair of parallel sides (usually the top and bottom). This means that its diagonals will never intersect; they always lie outside of one another’s lines.
A kite is essentially half of a bow tie laid flat on the ground, which is where it gets its two flaps. Its parallel sides are both right angles, which means it has five total.
A trapezium is a quadrilateral with no parallel sides (the top and bottom might be parallel to one another, but the left and right will never be). Like a trapezoid, there are no right angles in a trapezium.
A rhombus-like parallelogram that does have all four sides of equal lengths is known as a rhomboid. It’s important to note that while not technically incorrect, “rhombus” should only be used if the figure does not contain any straight lines – otherwise, it’s a rhomboid.
The area of a quadrilateral is defined as the area contained by the quadrilateral’s sides. The area of quadrilateral is measured in square units like m2, in2, cm2, and so forth. The method for calculating the area of a quadrilateral is dependent on the type of quadrilateral and the information available about it. If the quadrilateral does not correspond to one of the kinds listed above, we can calculate its area by splitting it into two triangles or by using the method for obtaining the area of a quadrilateral with four sides (called the Bretschneider′s formula). Here are the formulas for calculating the area of a quadrilateral that does not fit into any of the standard shapes.
A Real-life Example of Quadrilateral:
A real-life example of a quadrilateral is the shape of a room. The floor space between two walls in a room can be considered as a quadrilateral since there are four straight lines to form it, and the length and width are known for this quadrilateral. This would be an irregular quadrilateral because one pair of parallel sides do not exist (the side walls), but only one pair of congruent angles (angles along diagonals).