Question

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

Answer 1

Constructing the quadrilateral $\text{ABCD}$:

Let's draw a rough sketch of a parallelogram $\text{ABCD}$, to get an idea about the parallelogram -

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

$$\begin{gathered} \text{AB = 4.5 cm} \\ \text{AD = 6 cm} \\ \text{CD = 4 cm} \\ \text{AC = 7 cm} \\ \text{BC = 5.5 cm} \end{gathered}$$

Let's construct the parallelogram $\text{ABCD}$ using the information given in the question -

Step 1: Draw a line segment $\text{CD = 4 cm}$

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

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

.

Step 4: Join $\text{AB and BC}$ to get the required quadrilateral -

Hence, $\text{ABCD}$ is the required quadrilateral.