The bases of the trapezoid are 35 and 12, the side equal to 7 cm, forms an angle of 150
| July 7, 2021 | education
The bases of the trapezoid are 35 and 12, the side equal to 7 cm, forms an angle of 150 with one of the bases of the trapezoid. Find the area of the trapezoid.
From the top of an obtuse angle equal to 135 degrees, we lower the height CH to the base of AD.
In a right-angled triangle СНD, we determine the values of the angles. Angle НСD = ВСD – ВСН = 150 – 90 = 60. Then the angle СДН = 180 – 90 – 60 = 30.
The leg CH of a right-angled triangle CHD lies opposite the angle 30, therefore its length is equal to half the length of the hypotenuse CD.
CH = CD / 2 = 7/2 = 3.5 cm.
Determine the area of the trapezoid.
S = (AD + BC) * CH / 2 = (35 + 12) * 3.5 / 2 = 82.25 cm2.
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