The sides of the parallelogram are 5 cm and 4√3 cm, and one of the angles is 120 °. Find the area of the parallelogram.

Consider a parallelogram ABCD.
It is known:
AB = 4√3;
AD = 5, we draw the height BH.

It is known that triangle ABH is right-angled:
A = 180 – 120;
A = 60.
Find the angle ABH:
ABH = 90 – 60;
ABH = 30, leg AH lies opposite an angle of 30 °.
AB = 4√3 / 2;
AB = 2√3;
BH = √ (48 – 12);
BH = 6.
Find S:
S = 5 * 6;
S = 30.
Answer: S = 30.