# In an isosceles trapezoid ABCD smaller ACD = 135 о, AD = 20 cm, BC = 10 cm.Find the perimeter of the trapezoid.

We draw from the top of the trapezium C the height C, then the angle DСН = ВСD – ВСН = 135 – 90 = 45.

Then in the right-angled triangle СDН the angle СDН = 180 – 90 – 45 = 45, and therefore the triangle DH is isosceles, СН = DH.

The height of an isosceles trapezoid drawn to the larger base, we divide it into two segments of the length of the smaller of which is equal to the half-difference of the bases of the trapezoid. DH = (AD – BC) / 2 = (20 – 10) / 2 = 5 cm. Then CD = DH = 5 cm. Since the trapezoid is isosceles, AB = CD = 5 cm.

Let’s define the perimeter of the trapezoid. P = AB + BC + CD + AD = 5 + 10 + 5 + 20 = 40 cm.

Answer: The perimeter of the trapezoid is 40 cm.

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