ABCD-trapezoid. AB = 6, BC = 5, KD = 3, angle A = 60 degrees, BH belongs to AD, CK belongs

univerkov | September 11, 2021 | education

ABCD-trapezoid. AB = 6, BC = 5, KD = 3, angle A = 60 degrees, BH belongs to AD, CK belongs to AD a) What is the segment BH called? b) Find AD and P ABCD.

In a right-angled triangle ABН, the angle ABН = 180 – 90 – 60 = 30, then the leg AH is equal to half the length of the hypotenuse AB. AH = AB / 2 = 6/2 = 3 cm.

Since the segments AH and DK, cut off by the heights BH and СK, are equal from the base AD, the trapezoid ABCD is isosceles, then CD = AB = 6 cm.

Determine the length of the base AD. AD = AH + НK + DK = 3 + 5 + 3 = 11 cm.

Determine the perimeter of the trapezoid Ravsd = AB + BC + CD + AD = 6 + 5 + 6 + 11 = 28 cm.

Answer: BH is the height of the trapezoid, the length of AD is 11 cm, the perimeter of the trapezoid is 28 cm.

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