The diagonal of the parallelogram is 8 cm. The angle between this diagonal and the side

The diagonal of the parallelogram is 8 cm. The angle between this diagonal and the side of the parallelogram equal to 3 cm is 30 °, then the area of the parallelogram is.

1. The tops of the parallelogram – A, B, C, D. AB = 3 centimeters. BC = 5 centimeters. ∠ВАС = 30 °.

S – area.

2. From the vertex B of the triangle ABC we draw the height ВН.

3. We calculate its length through the sine ∠BAC:

ВН: AB = sine ∠ BAC = sine 30 ° = 1/2.

BH = AB x 1/2 = 3 x 1/2 = 1.5 centimeters.

4. S ΔАВС = ВН х ВС / 2 = 1.5 х 8/2 = 6 centimeters².

5. 3. The diagonal BC divides the parallelogram into two equal triangles:

ΔABС and ΔAСD. With this in mind, we calculate the area of the parallelogram:

6. S parallelogram AВСD = 6 х 2 = 12 centimeters².