From the vertices B and C we will construct the heights BK and CH. A quadrilateral BСHK is a rectangle, then KH = BC = 6 cm, and triangles ABK and CDH are rectangular.
By the Pythagorean theorem, we determine the lengths of the legs AK and DH.
AK ^ 2 = AB ^ 2 – BK ^ 2 = 25 – 16 = 9.
AK = 3 cm.
DH ^ 2 = CD ^ 2 – CH ^ 2 = 41 – 16 = 25.
DН = 5 cm.
Then AD = AK + KH + DH = 3 + 6 + 5 = 14 cm.
Determine the area of the trapezoid.
Savsd = (BC + AD) * BK / 2 = (6 + 14) * 4/2 = 40 cm2.
Answer: The area of the trapezoid is 40 cm2.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.