How to Construct a Quadrilateral

To build a quadrilateral, one must first understand its qualities. It is made up of four straight sides. Quadrilaterals can be classified based on the length of their sides and the magnitude of their angles. Squares, rectangles, rhombuses, parallelograms, trapezoid(trapezium), kites, and other irregular shapes belong to the quadrilateral family.

Quadrilateral

Polygons form quadrilaterals. They are a four-sided plane (quad means four and lateral means side). There are four sides and four angles on every quadrilateral. They can be categorised based on the lengths of their sides or angles. Squares, rectangles, trapezoids, rhombuses, parallelograms, and kites are examples of quadrilateral shapes (also called a tangential quadrilateral). It is a quadrilateral if all four sides are connected by straight lines. It’s not necessary for it to take on a specific shape.

Lines that link opposite angles are known as diagonals. Perpendicular diagonals and parallel sides are used to divide quadrilaterals.

A quadrilateral is a four-sided geometric shape with four vertices and four straight sides. It is a polygonal shape. The word ‘quadrilateral’ comes from the Latin words ‘quadri’, which means’four,’ and ‘latus,’ which means’side.’

Scalene quadrilateral

A scalene quadrilateral is the first type of quadrilateral. A quadrilateral with no unique qualities is known as a scalene quadrilateral. The lengths and measurements of the sides and angles vary.

Methods to construct a quadrilateral

We will study how to make a quadrilateral in construction of Quadrilaterals. A quadrilateral is made up of ten parts: four sides, four angles, and two diagonals. We’ll need information on five specific parts of a quadrilateral to build it. We’ll look at the five scenarios below and use an example to describe the structure. The needed quadrilateral is divided into two triangles that are easily produced.

Draw a quadrilateral ABCD with the following measurements: AB=4.8cm, BC=4.3 cm, CD=3.6cm, AD=4.2 cm, and diagonal AC=6cm.

Steps of Construction

 Step 1: Construct  AB= 4.8 cm .

Step 2: Draw an arc with A as the centre and a radius of 6 cm.

Step 3: Draw another circle with B as the centre and a radius of 4.3 cm, cutting the previous arc at C.

Step 4: join BC.

Step 5: Draw an arc with A as the centre and a radius of 4.2 cm.

Step 6: Draw another circle with Cas the centre and a radius of  3.6 cm, cutting the previous arc at D.

Step 7: Bring AD and CD together.

The needed quadrilateral is then ABCD.

Example of Quadrilateral

In reality, there are endless quadrilaterals! A quadrilateral is anything that has four sides, even if they are unequal. Table tops, books, picture frames, doors, baseball diamonds, and so on are all possible examples. Quadrilaterals come in a variety of shapes, some of which are more difficult to come by in real life, such as the trapezoid.

Steps for Constructing a quadrilateral

Construct quadrilaterals when four sides and one diagonal is given.

Construct a quadrilateral PQRS where PQ=4cm, OQ=6cm, RS=5cm, PS=5.5cm and PR=7cm.

• PQR should be drawn with SSS construction.

• Construct an arc of radius 5.5cm with Pas the centre.

• Make a 5-cm-radius arc with R at the centre.

• The place where the two arcs meet is called S. Mark S and finish PQRS as well.

• The quadrilateral PQRS is necessary.

Assume that out of the six parts of the triangle, any three are known. For quadrilateral construction, some of the quadrilateral’s measurements must be known. Because the quadrilateral contains four sides, four angles, and two diagonals, it is referred to as a four-sided figure.

To create a unique quadrilateral, four measurements are insufficient. 5 quadrilateral measures are required to draw a unique quadrilateral. As a result, if five measures of a quadrilateral are known, a quadrilateral can be drawn. If you offer five measures to a quadrilateral, you can design a unique quadrilateral. Four sides, four angles, and two diagonals make up a quadrilateral. When any four pieces of a quadrilateral are known, it’s impossible to draw a unique quadrilateral. A unique quadrilateral can be drawn if the five parts of a quadrilateral are known.

Conclusion

Given that three measurements are sufficient to draw a triangle, it’s only natural to wonder if four measurements would be sufficient to create a unique four-sided closed form, a quadrilateral. there are ten parts to a quadrilateral: four sides, four angles, and two diagonals. As a result, we’ll require data from at least five pieces to create a quadrilateral. We begin by sketching a rough quadrilateral and writing the measurements of the five parts of the quadrilateral in the rough drawing. The quadrilateral is then drawn when the data is analysed (measurements).

We divide the required quadrilateral into two easily created triangles. A quadrilateral will be formed by joining these two triangles.