Question

Construct a quadrilateral $ABCD$ in which $AB = 5.5cm,AD = 4.4cm,CD = 6.5cm,AC = 6.5cm$ and $BD = 7.1cm$ .

Answer 1

Hint: In this question, we are given lengths of sides and lengths of diagonals of a quadrilateral and we have to construct this quadrilateral.
For this, first we will draw the base $AB = 5.5cm$ , using ruler and pencil, then using ruler and compass, first we will mark an arc by keeping the compass tip at point $A$ which will be the side $AD$ then another arc from point $B$ on top of that arc only which will be the diagonal $BD$ . Similarly, follow the steps for side $BC$ and diagonal $AD$ and join them.
Let’s see steps one- by- one to construct this quadrilateral.

Complete answer:
We are given lengths of sides and lengths of diagonals of a quadrilateral $ABCD$ .
To construct the quadrilateral using these measurements.
First, draw the base $AB$ of the quadrilateral.

Now, open the compass by $4.4cm$ and put tip at $A$ , and mark an arc.

Now, open the compass by $BD = 7.1cm$ and put the tip at $B$ and mark an arc on the previous arc and name the intersecting point as $D$ .

Now, join point $D$ with $A$ and $B$ .

Now, similarly, open the compass by $6.5cm$ and put the compass on $A$ and mark an arc.

Now, put the compass on $D$ with same opening and name the intersecting point as $C$ .

Now, join $C$ with $D$ , $A$ and $B$ .

Hence, this is the required quadrilateral.

Note: In this way, we can find the length of the side $BC$ also. Similarly, we can construct a quadrilateral even if the measurements of angles and a side is given. A quadrilateral is polygon in which there are total four sides, ‘quad’ means ‘four’. Measurements should be exact while opening the compass and marking the arcs. Follow the steps carefully in order to avoid any mistake.