Construction of Quadilaterals

Quadrilaterals belong to the polygon family of Geometric Shapes. In this article, we will see the Construction of Quadrilaterals. First, we will see the different types of quadrilaterals which will help us better to understand the construction of Quadrilaterals.

Different Types of Quadrilaterals

Square: –

A Square is a closed two-dimensional Geometric Shape that consists of four vertices connected by four sides. The square has all four sides of equal length. In the square, all the angles are equal to 90°. 

If one side of a square is equal to a,

The Perimeter (P) of the square of side a,

P=a+a+a+a

P=4*a

P=4a

The Area (A) of the square of side a,

A=a*a

A=a2

This is the figure pertaining to a square.

Rectangle: – 

A rectangle is a two-dimensional geometric shape that consists of four vertices connected by four sides. In the rectangle, two of the four sides are equal in length to each other and the other two sides are equal to each other. All the angles in a rectangle are 90°.

If the measure of one side is a and the measure of the other side is b,

Then the Perimeter (P) of the Rectangle is,

P=a+b+a+b

P=2*a + 2*b

P=2(a+b)

The Area (A) of the Rectangle is,

A=a*b

A=ab

This is the figure pertaining to a rectangle.

Rhombus: – 

The rhombus is a closed two-dimensional geometric figure which consists of four vertices connected by four sides. The difference between a rhombus and a square is that a rhombus is diamond-shaped. All the sides of a rhombus are equal in measure and all the angles of a rhombus are also equal in measure (90°).

If one side of the rhombus is equal to a,

The Perimeter (P) of the rhombus is,

P=a+a+a+a

P=4*a

P=4a

If the diagonals of the rhombus are equal to d1 and d2,

The Area (A) of The Rhombus is,

A= (1/2)*(d1)*(d2)

The above figure pertains to a Rhombus.

Parallelogram: – 

The Parallelogram is a closed two-dimensional geometric shape which consists of four vertices connected by four sides. The opposite sides of a parallelogram are parallel and of equal measure in length. 

In order to find out the area of the parallelogram, drop a perpendicular from one vertex on to the opposite side. 

Let the length of the perpendicular be equal to h and let the length of one the sides be equal to b and let the length of the other sides be equal to a.

Then the Perimeter (P) of the Parallelogram is equal to,

P=2(a+b)

Then the area (A) of the parallelogram is equal to,

A=bh

This is the figure pertaining to a parallelogram.

Conditions for the Construction of Quadrilaterals

There are a few cases in which a quadrilateral can be constructed:-

1. If we are given the lengths of the four sides are given and we are the length of the diagonal in the question.

2. In the question, they give us the length of two diagonals and they give us the length of the three sides of the quadrilateral.

3. If in the question they give us the length of two adjacent sides and the measures of three angles of the quadrilateral.

4. If we are given the length of three sides and the measure of two included angles of a quadrilateral in the question.

5. If the question specifies any of the special properties of a quadrilateral.

Construction of Quadrilaterals-

Now we will see how to construct a quadrilateral using the four conditions given above.

1. If the question gives us the lengths of the four sides and the length of the diagonal, first we have to draw a rough sketch just for the sake of representation purposes only. Then draw the lines and the diagonal according to the measurements given in the question. For the construction of the quadrilateral, construct a triangle using the diagonal and one of the remaining two points. This triangle can be constructed with the help of SSS property. When we have the triangle, it is very easy to find the fourth point using the measurements already given. For e.g. If we draw a triangle PQR with PR as the diagonal and Q as one of the vertices. So if we draw an arc with P as the center and another arc with R as the center we can get another point S. That will give us our quadrilateral PQRS.

2. If in the question, they give us the lengths of two diagonals, first we draw the rough diagram of the quadrilateral for representation. We can draw a triangle as we did in the first method. Suppose we have considered a quadrilateral ABCD. Then we construct a triangle ACD with AC being the diagonal. Then we draw an arc with C as the center and another one with D as the center. Then we join D with the meeting point of the two arcs. We have our quadrilateral. 

3. This method is very simple as we will get our quadrilateral simply by following the instructions given in the question.

4. In this method, we can very easily get the quadrilateral just by following the instructions.

5. We can get the quadrilateral by using the special property of the quadrilateral.

Conclusion

In this article, we talked about the quadrilateral. Then we moved on to talking about the types of quadrilaterals. We have discussed square, rhombus, rectangle and parallelogram which are different types of quadrilaterals. We also learnt the formulae to calculate the area and perimeter of each of those quadrilaterals. Then we finally discussed the conditions of constructing a quadrilateral and how to construct a quadrilateral.