The side of the rhombus is 10 dm and its obtuse angle is 150 degrees, find the area of the rhombus.

Given:
ABCE – rhombus,
BC = 10 decimeters,
angle B = 150 degrees.
Find the area of the rhombus ABCE, that is, S ABCE -?
Decision:
1. Consider a rhombus ABCE. It has opposite sides and angles are equal to each other, then angle A = angle C, angle B = angle E. We know that the sum of the degree measures of the parallelogram is 360 degrees. Hence:
angle A + angle C = 360 – 150 – 150;
angle A + angle C = 60;
angle A = angle C = 60: 2;
angle A = angle C = 30 degrees.
2. S ABCE = BC * CE * sin C;
S ABCE = 10 * 10 * 1/2;
S ABCE = 10 square decimeters.
Answer: 10 square decimeters.