Find the area of a rectangular trapezoid, the acute angle of which is 30 degrees, and the large lateral side is 8 cm
| September 16, 2021 | education
Find the area of a rectangular trapezoid, the acute angle of which is 30 degrees, and the large lateral side is 8 cm, if a circle can be inscribed into this trapezoid.
From the vertex C of the trapezoid ABCD, we will construct the height CH.
In a right-angled triangle CDH, the CH leg lies opposite an angle of 30, then CH = CD / 2 = 8/2 = 4 cm.
Quadrangle СBАН is a rectangle, then AB = CH = 4 cm.
Since, by condition, a circle can be inscribed into a trapezoid, the sum of the lengths of the opposite sides of the trapezoid are equal.
BC + AD = AB + CD = 4 + 8 = 12 cm.
Determine the area of the trapezoid.
Savsd = (ВС + АD) * СН / 2 = 12 * 4/2 = 24 cm2.
Answer: The area of the trapezoid is 24 cm2.
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