Question

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

Answer 1

Given $DE=4cm,EA=5cm,AR=4.5cm,\angle E={60}^{\circ },\angle A={90}^{\circ }$

To construct: A quadrilateral $DEAR$.

Steps of construction:

(a) Draw a line segment $DE=4cm$.

(b) At point $E$, construct an angle of ${60}^{\circ }$ using a protractor.

(${60}^{\circ }$ can also be constructed with the help of a compass. With $E$ as centre and appropriate radius, draw a semi circle on the point $E$. On the semi circle, with same radius, cut two arcs. The line passing through the first arc and point $E$ is ${60}^{\circ }$ )

(c) Taking radius $5cm$, draw an arc from point $E$ which intersects at $A$.

(d) Construct $\angle A={90}^{\circ }$ using a protractor, draw an arc of radius $4.5cm$ with centre$A$ which intersects at $R$.

($\angle A={90}^{\circ }$ can also be constructed the help of a compass. Repeat the steps for ${60}^{\circ }$. Now bisect the two arcs so formed to get $\angle A={90}^{\circ }$).

(e) Join $RD$.

It is the required quadrilateral $DEAR$.