In trapezoid ABCD, side AD is larger than the base. a straight line is drawn through the vertex C
| June 17, 2021 | education
In trapezoid ABCD, side AD is larger than the base. a straight line is drawn through the vertex C parallel to AB, up to the intersection with AD at point E; AE = 3 cm; ED = 9 cm; Pecd = 22 cm. Find the perimeter of the trapezoid.
Consider the quadrilateral ABCE.
By condition, AB is parallel to CE, and BC is parallel to AE as the base of the trapezoid, then the quadrilateral is a parallelogram. BC = AE = 3 cm, AB = CE.
The perimeter of the trapezoid is: Ravsd = AB + BC + AE + DE.
Since AB = CE, then Ravsd = CE + BC + CD + AE + DE.
The sum (CE + CD + DE) is equal to the perimeter of the triangle CDE, then:
Ravsd = Rsde + BC + AE = 22 + 3 + 3 = 28 cm.
Answer: The perimeter of the trapezoid is 28 cm.
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