Question

Construct the quadrilaterals with the given measurements and write steps of construction.
quadrilateral $ABCD$ with $AB=5.5cm$,$BC=3.5cm$,$CD=4cm$,$AD=5cm$ and $\angle A={45}^{\circ }$

Answer 1

Given that ,

$AB=5.5$, $BC=3.5$, $CD=4$, $AD=5CM$

Steps of Construction:

Step 1 :

Draw a rough sketch of the required quadrilateral and mark the given measurements.

Step 2 :

Draw $\Delta DAB$ using S.A.S property of construction , by taking $AD=5cm,\angle DAB={45}^{\circ }$ and $AB=5.5cm$.

Step 3 :

To locate the fourth vertex ‘$C$’, draw an arc , with center $D$ and radius $4cm,(CD=4cm)$.

Draw another arc with center $B$ and radius $3.5cm(BC=3.5cm)$ which cuts the previous arc at $C$.

Step 4:

Join $DC$ and $BC$ to complete the required quadrilateral $ABCD$.

Hence, $ABCD$ is the required quadrilateral.