The angle of the isosceles trapezoid is 135 degrees and the height is 3 cm.

| April 12, 2021 | education

The angle of the isosceles trapezoid is 135 degrees and the height is 3 cm. Calculate the perimeter of the trapezoid if the length of the smaller base is 2 cm.

Since BH is the height of the trapezoid, the triangle ABH is rectangular. Then the angle ABH = ABC – СBH = 135 – 90 = 45.

Angle BAC = ABH = 45, then triangle ABH is isosceles and right-angled.

Then AB = BH = 3 cm.

Let us determine the length of the hypotenuse AB. AB = AH / Cos45 = 3 / (√2 / 2) = 6 / √2 = 3 * √2 cm.

Since the trapezoid is isosceles, then CD = AB = 3 * √2 cm.

Let’s draw the height of the CК.

Segment KD = AH = 3 cm, since the trapezoid is isosceles.

НК = ВС = 2 cm, then АD = АН + НК + DH = 3 + 2 + 3 = 8 cm.

Determine the perimeter of the trapezoid.

P = AB + BC + CD + AD = 3 * √2 + 2 + 3 * √2 + 8 = 10 + 6 * √2 cm.

Answer: The perimeter of the trapezoid is 10 + 6 * √2 cm.



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