Question

construct a quadrilateral ABCD with AB = 6cm, AD = 6cm, angle ABD = 45° angle BDC = 40° and angle DBC = 40°​

Answer 1

Refer to the attachment for diagram !!

And refer below for steps...

• Step 1 : Draw a rough diagram and mark the given measurements.
• Step 2 : Draw a line segment AB = 6 cm.
• Step 3 : At B on AB make ∠ ABX whose measure is 45o .
• Step 4 : With A as centre and 6 cm as radius draw an arc. Let it cut $$\overline{BX}$$ at D.
• Step 5 : Join AD .
• Step 6 : At B on BD make ∠ DBY whose measure is 40o .
• Step 7 : At D on BD make ∠ BDZ whose measure is 40o .
• Step 8 : Let BY and DZ intersect at C. ABCD is the required quadrilateral.
• Step 9 : From A draw AE⊥BD and from C draw CF⊥BD. Then measure the lengths of AE and CF. AE = h−1 = 4.2 cm, CF = h2 = 3.8 cm and BD = d = 8.5 cm.

Calculation of area:

In the quadrilateral ABCD, d = 8.5 cm, h1 = 4.2 cm and h2 = 3.8 cm.

Area of the quadrilateral ABCD = 21d(h1+h2)

 =21