In a parallelogram, the acute angle is 30 degrees; the bisector of this angle divides the side into segments 14 and 9 cm

| May 19, 2021 | education

In a parallelogram, the acute angle is 30 degrees; the bisector of this angle divides the side into segments 14 and 9 cm, counting from the apex of the obtuse angle. Find the area of a parallelogram.

Let ABCD be a parallelogram, the bisector AM is drawn from the angle A = 30 ° (BAM = MAD = 15 °), so that BM = 14 cm, MC = 9 cm.

By the property of a parallelogram, the sum of adjacent angles is 180 °, i.e. ABC + BAD = 180 °, whence ABC = 180 – 30 = 150 °.

Consider ΔАВМ: BAM = 15 °, ABC = 150 °. Then BMA = 180 – BAM – ABC = 180 – 150 – 15 = 15 °.

Because BAM = BMA = 15 °, therefore ΔABM is an isosceles triangle, BM = AB = 14 cm.

AD = BC = BM + MS = 9 + 14 = 23 cm.

Let’s calculate the area of the parallelogram:

S = a * b * sinα, where a = AB = 14, b = AD = 23, α = A = 30.

S = 14 * 23 * sin30 = 161.



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