In a parallelogram, the obtuse angle is 150. The bisector of this angle divides the side of the parallelogram into segments 16 and 5 cm, counting from the apex of the acute angle. Find the area of the parallelogram.
1. A, B, C, D – the tops of the parallelogram. Angle B = 150 °. AK = 16 cm.DK = 5 cm.
2. The bisector BK of the parallelogram cuts off the isosceles triangle ABK from it.
Therefore, AB = AK = 16 cm.
3. Angle A = 180 ° – 150 ° = 30 °.
4. Draw the height BH to the AD side.
5. The leg BH is equal to half of the hypotenuse AB, since in a right-angled triangle ABH
is opposite an angle of 30 °:
BH = 16: 2 = 8 cm.
5.AD = AK + DK = 16 + 5 = 21 cm.
6. Area of the parallelogram ABCD = AD x BH = 21 x 8 = 168 cm ^ 2.
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