The diagonal of the parallelogram, equal to 18 cm, is perpendicular to one of its sides and forms an angle

The diagonal of the parallelogram, equal to 18 cm, is perpendicular to one of its sides and forms an angle of 30 degrees with the other side. Find the area of a parallelogram.

1. Vertices of the parallelogram – А, В, С, D. ВD – diagonal. ∠ADB = 30 °.

2. We calculate the length of the side AB through the tangent ∠ADB:

AB: BD = tangent ∠ADB = tangent 30 ° = √3 / 3.

AB = BD x √3 / 3 = 18 x √3 / 3 = 6√3 centimeters.

3. Calculate the area S of the triangle ABD:

S ΔABD = AB x BD / 2 = 6√3 x 18/2 = 54√3 centimeters².

4. Diagonal BD divides the parallelogram into two equal triangles:

ΔABD and ΔBCD. With this in mind, we calculate the area of the parallelogram:

S parallelogram ABCD = 54√3 x 2 = 108 √3 centimeters².