Question

Construction of quadrilaterals when three sides and two diagonals are given:
2. Construct a quadrilateral ABCD in which AB = 4 cm BC = 3.8 cm, AD = 3 cm, diagonal AC = 5 cm and diagonal BD = 4.6 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 $\Delta ABD$. (Rough Sketch) $\to$
Steps of Construction:

Step 1: Draw AB = 4 cm.
Step 2: With A as center and radius equal to 5 cm, draw an arc.
Step 3: With B as center and radius equal to 3.8 cm, draw another arc, cutting the previous arc at C.
Step 4: Join BC.
Step 5: With A as center and radius equal to 3 cm, draw an arc.
Step 6: With B as center and radius equal to 4.6 cm draw another arc, cutting the previous arc at D.
Step 7: Join AD and CD.
Then, ABCD is the required quadrilateral.