In the parallelogram ABCD, the degree measure of the angle CDA is 150 degrees, and the distance from the vertex D to line AB is 4 cm. Calculate the lengths of the sides of a parallelogram if its perimeter is 42.
Since the degree measure of the angle CDA = 150 °, we can conclude that the degree measure of the angle BAD = 150 ° – 180 ° = 30 °.
The distance from vertex D to line AB is the height for the parallelogram, thus forming a right triangle, and side AD will be 2 * height, since the height lies t against an angle of 30 °.
AD = 2 * 4 = 8
AD = BC = 8
AB = CD = (42 – (2 * 8)) / 2 = 13
Answer: 8, 13, 8, 13
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