Question

What is the perimeter of the quadrilateral ABCD?

Answer 1

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,

$\angle DAB\cong \angle ABD$               [Given]

$\Delta ABD$ is an isosceles triangle      [Base angle property]

$AD=BD$                   [By definition of isosceles triangles]    

$8=BD$                   ...(i)

In triangle BCD,

$\angle BCD\cong \angle CDB\cong \angle CBD$        [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.

$BC=CD=BD$

$BC=CD=8$      [Using (i)]               ...(ii)

Now, the perimeter of quadrilateral ABCD is:

$Perimeter=AB+BC+CD+AD$

$Perimeter=11+8+8+8$

$Perimeter=35$

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