Given an isosceles trapezoid ABCD. It is known that AB = CD (sides are equal)

| May 30, 2021 | education

Given an isosceles trapezoid ABCD. It is known that AB = CD (sides are equal) and BC = 3cm (base) and AD = 7cm (base) CA is the bisector of angle C. Find, P trapezoid.

The perimeter of a given trapezoid can be found using the following formula:

P = AB + BC + CD + AD.

We know the lengths of the sides BC and AD. It remains to find the sides BC and CD. They are equal.

Consider a triangle ACD. It is known that AC divides the angle C in half. Hence ACB angle = ACD angle. Also ACB angle = CAD angle, as cross overlapping angles. This means that the triangle ACD is isosceles, where AD = CD = 7 cm.

Now we know the lengths of all sides, and we can find the perimeter of the trapezoid. Let’s calculate it:

P = 7 + 3 + 7 + 7 = 24 cm.

Answer: the perimeter of the trapezoid is 24 cm.



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