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Question

Construct the following quadrilateral: Quadrilateral DEAR,DE=4cm,EA=5cm,AR=4.5cm,∠E=60°,∠A=90°.


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Solution

Constructing the quadrilateral DEAR:

Let's draw a rough sketch of DEAR, to get an idea of the quadrilateral -

∠A=90°∠E=60°DE=4cmEA=5cmAR=4.5cm

Let's draw the quadrilateral using the given information -

Step 1: Draw a line segment EA=5cm, and draw the angle a ray EXandAY making an angle of 60°and90°respectively

Step 2: Take an arc of radius 4cm on the compass and cut an arc on ray EX at D, then change the radius to 4.5cm on the compass and cut an arc on ray AY at R

Step 3: Join RD, to get the required quadrilateral

Hence, DEAR is the required quadrilateral.


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