In an isosceles trapezoid, the side, height and diagonal are equal to the root of 117,9,15, respectively.
| August 29, 2021 | education
In an isosceles trapezoid, the side, height and diagonal are equal to the root of 117,9,15, respectively. find the area of the trapezoid
From the right-angled triangle ABK, according to the Pythagorean theorem, we determine the length of the leg AK.
AK ^ 2 = AB ^ 2 – BK ^ 2 = 117 – 81 = 36.
AK = 6 cm.
In a right-angled triangle ВDК, according to the Pythagorean theorem, we determine the length of the leg DК.
DK ^ 2 = BD ^ 2 – BK ^ 2 = 225 – 81 = 144.
DK = 12 cm.
Since the trapezoid is isosceles, then DH = AK = 6 cm.
Base length AD = AK + DK = 6 + 12 = 18 cm.
KN = DK – AK = 12 – 6 = 6 cm, then BC = KН = 6 cm.
Determine the area of the trapezoid.
Savsd = (ВС + АD) * СK / 2 = (6 + 18) * 9/2 = 108 cm2.
Answer: The area of the trapezoid is 108 cm2.
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