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Question

Construct the following quadrilateral: Quadrilateral ABCD where AB=4.5cm, BC=5.5cm, CD=4cm, AD=6cm and AC=7cm.


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Solution

Constructing the quadrilateral ABCD:

Let's draw a rough sketch of a parallelogram ABCD, to get an idea about the parallelogram -

By the properties of the parallelogram, we know that opposite sides are equal, therefore

AB=4.5cmAD=6cmCD=4cmAC=7cmBC=5.5cm

Let's construct the parallelogram ABCD using the information given in the question -

Step 1: Draw a line segment CD=4cm

Step 2: Take an arc of radius 6cm on the compass & cut an arc from point D, then change the radius to 7cm and cut another arc from point C which intersect the previous arc at point A and then join ADandAC

Step 3: Take an arc of radius 5.5cm on the compass & cut an arc from point C, then change the radius to 4.5cm and cut another arc from point A which intersect the previous arc at point B

.

Step 4: Join ABandBC to get the required quadrilateral -

Hence, ABCD is the required quadrilateral.


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