Question

Quadrilaterals WXYZ and BADC are congruent. In addition, WX ≅ DC and XY ≅ BC.

If AD = 4 cm and AB = 6 cm, what is the perimeter of WXYZ?

18 cm
20 cm
22 cm
24 cm

Answer 1

Refer to the diagram shown below.

Because quads WXYZ and BADC are congruent, therefore
WX = BA = 6 cm
XY = AD = 4 cm
YZ = DC
WZ = BC

Because WX = DC, therefore WX = DC = YZ = 6 cm
Because XY = BC, therefore XY = BC = WZ = 4 cm

Therefore the sides of WXYZ are
XY = 4 cm
YZ = 6 cm
WZ = 4 cm
WX = 6 cm

The perimeter of WXYZ is
4 + 6 + 4 + 6 = 20 cm

Answer: 20 cm