In an isosceles trapezoid, the diagonal is the bisector of an obtuse angle and divides the midline

| June 20, 2021 | education

In an isosceles trapezoid, the diagonal is the bisector of an obtuse angle and divides the midline into segments 5.5 cm and 12.5 cm long. Find the area of the trapezoid.

In triangle ABC, the segment KO is parallel to BC, and point K is the middle of AB, then KO is the middle line of the triangle, and then BC = 2 * KO = 2 * 5.5 = 11 cm.

Similarly, in the ACD triangle, AD = 2 * MO = 2 * 12.5 = 25 cm.

Since AC is the bisector of the angle BCD, the triangle ACD is isosceles and CD = AD = 25 cm.

Since the trapezoid is isosceles, the segment DH is equal to the half-difference of the lengths of the trapezoid bases.

DН = (АD – ВС) / 2 = (25 – 11) / 2 = 7 cm.

From the right-angled triangle СDН, we determine the length of the leg СН.

CH ^ 2 = CD ^ 2 – DH ^ 2 = 625 – 49 = 576.

CH = 24 cm.

Determine the area of ​​the trapezoid.

Savsd = (ВС + АD) * СН / 2 = (11 + 25) * 24/2 = 432 cm2.

Answer: The area of ​​the trapezoid is 432 cm2.



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