The bases of an isosceles trapezoid are 10cm and the side 20cm is 14cm, one of the corners is 150 °. Find the area of the trapezoid.

univerkov | January 13, 2021 | education

Let’s draw from the top of the obtuse angle B of the trapezium AВСD the height ВН. In the resulting right-angled triangle, we determine the values of the angles AВН and AНВ.
Angle ABН = 150 – 90 = 60.
Angle AНВ = 180 – 90 – 60 = 30.
The height of the ВН lies opposite the angle of 300, therefore, it is equal to half the length of the hypotenuse AB.
BH = AB / 2 = 14/2 = 7 cm.
Determine the area of the trapezoid.
S = (BC + AD) * ВН / 2 = (10 + 20) * 7/2 = 105 cm2.
Answer: The area of the trapezoid is 105 cm2.

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