What is the perimeter of the quadrilateral ABCD?

Given:

The figure of a quadrilateral ABCD.

To find:

The perimeter of the quadrilateral ABCD.

Solution:

In an isosceles triangle, the two sides and base angles are congruent.

In triangle ABD,

              [Given]

is an isosceles triangle      [Base angle property]

                  [By definition of isosceles triangles]    

                  ...(i)

In triangle BCD,

       [Given]

All interior angles of the triangle BCD are congruent, so the triangle BCD is an equilateral triangle and all sides of the triangle area equal.

     [Using (i)]               ...(ii)

Now, the perimeter of quadrilateral ABCD is:

Therefore, the perimeter of the quadrilateral ABCD is 35 units.