Find the area of the trapezoid if the bases are 30 cm and 40 cm, the obtuse angle is 150 degrees, the lateral side is 20 cm.

univerkov | May 15, 2021 | education

1. The tops of the trapezoid – A, B, C, D. ∠B = 150 °. BC = 30 cm AD = 40 cm AB = 20 cm BE – height.

S is the area of the trapezoid.

2. ∠ABE = ∠B – ∠CBE = 150 ° – 90 ° = 60 °.

3. We calculate the length of the height BE through the cosine ∠ABE, equal to the ratio of the height of BE, which is a leg in a right-angled triangle ABE, to the hypotenuse AB of the indicated triangle:

BE / AB = cosine ∠ABE = cosine 60 ° = 1/2.

BE = AB x 1/2 = 20 x 1/2 = 10 cm.

S = (AD + BC) / 2 x BE = (40 + 30) / 2 x 10 = 350 cm².

Answer: S is equal to 350 cm².

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