In a parallelogram, the acute angle is 30 degrees. The bisector of this angle divides the side of the parallelogram into segments of 14 cm and 6 cm, counting from the top of the acute angle. Find the area of the parallelogram.
1. A, B, C, D – the tops of the parallelogram. AH is the bisector. BH = 6 cm. CH = 14 cm. Angle A = 30 °.
ВH – height.
2. The bisector AH of the parallelogram ABCD cuts off the isosceles triangle ABH from it.
AB = BH = 6 cm.
3. In a right-angled triangle ABH, the height BH is the leg opposite an angle of 30 °. Therefore, its length is half the length of the hypotenuse AB.
BH = AB: 2 = 6: 2 = 3 cm.
5. BC = BH + CH = 6 + 14 = 20 cm.
6. Area of the parallelogram ABCD = BC x BH = 20 x 3 = 60 cm ^ 2.
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