Question

Construct the quadrilateral DEAR, DE=4 cm, EA=5 cm, AR=4.5 cm, $\angle E={{60}^{\circ }}$ and $\angle A={{90}^{\circ }}$.

Answer 1

Hint: We construct the quadrilateral given by first drawing the line EA using a ruler and given length 5cm. Then we use a protractor and draw a line at angle ${{90}^{\circ }}$ to EA. Then use a compass and draw an arc at length 4.5cm on the line and mark it as R. Then again use a protractor and draw line from point E, at angle ${{60}^{\circ }}$ and then draw an arc using a compass at length 4cm on that line and mark the intersecting point as D. Then join D and R to complete the quadrilateral.

Complete step-by-step answer:
First let us draw a rough sketch of the quadrilateral we need.

To construct the quadrilateral DEAR, first let us draw a line of 5cms and name the endpoints as EA.

Then use a protractor and place it point A and draw a line at angle ${{90}^{\circ }}$ with EA.

Now let us take a compass and use a ruler and take a length of 4.5cms and mark it on the line and name the point of intersection of arc and the line drawn above as R.

Now, let us use a protractor and place it on line AE and draw a line at an angle ${{60}^{\circ }}$.

Now let us take a compass and a ruler and take a length of 4cm and draw an arc on the line drawn above and name the point of intersection of line and the arc as D.
 

Now, join the points D and R. Then we get the quadrilateral DEAR.

So, we can construct any quadrilateral in the above manner.

Note: We can also start the construction of the quadrilateral by starting with drawing the line DE and then draw a line from point E, at angle ${{60}^{\circ }}$ and draw an arc with length 5cm and so on by following the similar steps as in the above or draw the line AR of length 4.5cm and then construct the quadrilateral.