The perimeter of the polygon is 143/6 cm or approximately 23.83 cm.
To find the length of AD, we can use the fact that opposite angles in a parallelogram are equal. Since ∠B ≅ ∠D, we can conclude that △ABD is similar to △CDB (by Angle-Angle similarity).
Let x represent the length of AD.
Using the properties of similar triangles:
AD/AB = DC/BC
So, x/5 = 7/6
Cross-multiplying, we get:
6x = 5 * 7
6x = 35
x = 35/6 cm
Now that we have found the length of AD, we can calculate the perimeter of the polygon by adding up all the sides:
Perimeter = AB + BC + CD + AD
Perimeter = 5 cm + 6 cm + 7 cm + 35/6 cm
Perimeter = 18 cm + 35/6 cm
Perimeter = 108/6 cm + 35/6 cm
Perimeter = (108 + 35) / 6 cm
Perimeter = 143/6 cm
So, the perimeter of the polygon is 143/6 cm or approximately 23.83 cm.