quadrilaterals wxyz and badc are congruent. in addition, $overline{wx}congoverline{dc}$ and…

Explanation:

Step1: Recall congruent - quadrilateral property

Since WXYZ and BADC are congruent, corresponding sides are equal.

Step2: Identify corresponding sides

We know that if two quadrilaterals are congruent, then (WX = DC), (XY=BC), (YZ = AD), (WZ=AB). Given (AD = 4\mathrm{cm}) and (AB = 6\mathrm{cm}), so (YZ = 4\mathrm{cm}) and (WZ = 6\mathrm{cm}). Also, from (\overline{WX}\cong\overline{DC}) and (\overline{XY}\cong\overline{BC}), the perimeter of (WXYZ) is the same as the perimeter of (BADC).

Step3: Calculate the perimeter of BADC

The perimeter (P) of a quadrilateral (BADC) with side - lengths (AB), (BC), (CD), (DA) is (P=AB + BC+CD + DA). Since (AB = 6\mathrm{cm}) and (AD = 4\mathrm{cm}), and for a quadrilateral, (P = 2(AB + AD)) (because of the congruence - related side - equalities). Substitute (AB = 6\mathrm{cm}) and (AD = 4\mathrm{cm}) into the formula: (P=2(6 + 4)). [P=2\times10=20\mathrm{cm}]

Answer:

20 cm