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

March 28, 2021 | education

| 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.

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