Question

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

Answer 1

Constructing the quadrilateral $\text{DEAR}$:

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

$$\begin{gathered} \text{∠A = 90°} \\ \text{∠E = 60°} \\ \text{DE = 4 cm} \\ \text{EA = 5 cm} \\ \text{AR = 4.5 cm} \end{gathered}$$

Let's draw the quadrilateral using the given information -

Step 1: Draw a line segment $\text{EA = 5 cm}$, and draw the angle a ray $\text{EX and AY}$ making an angle of $\text{60° and 90° respectively}$

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

Step 3: Join $\text{RD}$, to get the required quadrilateral

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