The acute angle of the parallelogram = 30 degrees, and the heights drawn

| May 5, 2021 | education

The acute angle of the parallelogram = 30 degrees, and the heights drawn from the top of the obtuse angle are 4cm and 6cm. Find the area of a parallelogram

1. Vertices of the parallelogram A, B, C, D. ∠A = 30 °. ∠В – stupid. Height ВK = 4 cm – drawn to the AD side. Height BE = 6 cm – drawn to the side of the CD.

2. In a right-angled triangle AВK, the leg ВK (parallelogram height) is opposite to ∠A, equal to 30 °. Therefore, according to the properties of this triangle, ВK = 1 / 2AB.

Hence, AB = 2x BK = 2 x 4 = 8 cm.

3. According to the properties of a parallelogram, its opposite sides are equal.

That is, AB = CD = 8 cm.

4. Calculate the area (S) of a given geometric figure:

S = CD x BE = 8 x 6 = 48 cm².

Answer: the area of ​​the parallelogram is 48 cm².



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