In a rectangular trapezoid, the larger base is 16 cm, the height is 6 cm, and the obtuse angle
| February 16, 2021 | education
In a rectangular trapezoid, the larger base is 16 cm, the height is 6 cm, and the obtuse angle is 135 degrees. Find the length of the midline of the trapezoid.
Since the CH is the height of the trapezoid, then the СDН triangle is rectangular, and the angle ВCH = 90, then the angle DСВ = ВСD – ВCH = 135 – 90 = 45.
The right-angled triangle СDН is isosceles, since one of its acute angle is 45, then CH = DН = 6 cm.
The length of the segment AH =AD- DН = 16 – 6 = 10 cm.
Since ABCН is a rectangle, the length of the base BC = AH = 10 cm.
Determine the length of the midline of the trapezoid.
KР = (BC + AD) / 2 = (10 + 16) / 2 = 13 cm.
Answer: The length of the middle line is 13 cm.
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