Question

Construct a parallelogram whose diagonal is $5.4\mathrm{cm}$ and $6.2\mathrm{cm}$ and an angle between them is $70°$.

Answer 1

Step 1. First, draw $AC=5.4\mathrm{cm}$.

Step 2. Then, bisect $AC$ at $O$.

Take A as a center make arcs on both sides of line and repeat same process with point C.

Now join the points where arcs meet with each other with dotted line.

Step 3. Make an angle $\angle COX={70}^{°}$ and produce $XO$ to $Y$.

With the help of protector make an angle of $\angle COX={70}^{°}$with the line $AC$

Step 4. With $O$ as a center, cut an arc $OB=\left(\frac{1}{2}·6.2\mathrm{cm}\right)3.1\mathrm{cm}$ and $OD=3.1\mathrm{cm}$ .

Step 5.Now, join $AB,BC,CD,\mathrm{and}DA$.

Hence, $ABCD$ is the required parallelogram as shown in the figure below: