ABCD parallelogram AD = 12 cm AB = 20 cm angle B = 150 degrees find the area ABCD.

univerkov | July 26, 2021 | education

1. According to the properties of a parallelogram, the total value of the angles that adjoin one of its sides is 180 °. Considering this, the angle BAD = 180 ° – 150 ° = 30 °.

2. Draw the BH height to the AD side.

3. In the formed triangle ABH, the height BH is a leg opposite an angle of 30 °. Therefore, its length is equal to 1/2 the length of the hypotenuse AB:

BH = AB: 2 = 20: 2 = 10 cm.

4. The area of the parallelogram = AD x AH = 12 x 10 = 120 cm ^ 2.

Answer: the area of the parallelogram ABCD = 120 cm ^ 2.

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