Question:
Construct a quadrilateral ABCD in which AB = 3.5 cm, BC = 3.8 cm, CD = DA = 4.5 cm and diagonal BD = 5.6 cm.
Solution:
Steps of construction:
Step 1: Draw $\mathrm{AB}=3.5 \mathrm{~cm}$.
Step 2: With B as the centre and radius equal to $5.6 \mathrm{~cm}$, draw an arc.
Step 3: With $A$ as the centre and radius equal to $4.5 \mathrm{~cm}$, draw another arc, cutting the previous arc at $D$.
Step 4: Join BD and AD.
Step 5: With D as the centre and radius equal to $4.5 \mathrm{~cm}$, draw an arc.
Step 6: With B as the centre and radius equal to $3.8 \mathrm{~cm}$, draw another arc, cutting the previous arc at C.
Step 7: Join BC and CD.
Thus, ABCD is the required quadrilateral.