Question

Construction of quadrilaterals when four sides and one diagonal are given:
1. Construct a quadrilateral ABCD in which AB = 4.8 cm, BC = 4.3 cm, CD = 3.6 cm, AD = 4.2 cm and diagonal AC = 6 cm.

Answer 1

First we draw a rough sketch of quadrilateral ABCD and write down its dimensions, as shown.
We may divide it into two triangles, namely $\Delta ABC$ and $\Delta ACD$. (Rough Sketch) $\to$
Steps of Construction:

Step 1: Draw AB = 4.8 cm.
Step 2: With A as center and radius equal to 6 cm, draw an arc.
Step 3: With B as center and radius equal to 4.3 cm, draw another arc, cutting the previous arc at C.
Step4: Join BC.
Step 5: With A as center and radius equal to 4.2 cm, draw an arc.
Step 6: With C as center and radius equal to 3.6 cm, draw another arc, cutting the previous arc at D.
Step 7: Join AD and CD.
Then, ABCD is the required quadrilateral.