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.