In parallelogram ABCD, the height BE is lowered from the vertex of obtuse angle B to side AD, with AE = ED

In parallelogram ABCD, the height BE is lowered from the vertex of obtuse angle B to side AD, with AE = ED. Find the area of the parallelogram if you know that angle A = 60 degrees and the height is 3√3.

1. We calculate the length of the segment AE through the tangent of the angle A:

BE: AE = tangent of angle A. Tangent 60 ° = √3.

AE = BE: √3 = 3√3: √3 = 3 units.

2. AE = DE by the problem statement. Therefore, the length DE is also 3 units.

3. AD = AE + DE = 3 + 3 = 6 units of measurement.

4. Area of the trapezoid = AD x BE = 6 x 3√3 = 18√3 units of measurement ^ 2.

Answer: the area of the trapezoid ABCD is equal to 18√3 units of measurement ^ 2.