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?

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frika frika · Answer 1 · 2018-11-12T10:03:35+01:00

If quadrilaterals WXYZ and BADC are congruent, then their corresponding sides are congruent.

Given that

you can state that

If AD = 4 cm and AB = 6 cm, then WZ = 4 cm and YZ = 6 cm. Opposite rectangle sides are congruent, then XY = 4 cm and WX = 6 cm.

The perimeter of WXYZ is

P = WX + XY + YZ + WZ = 6 + 4 + 6 + 4 = 20 cm.

Answer: 20 cm

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MrRoyal MrRoyal · Answer 2 · 2021-10-29T12:55:21+02:00

Congruent shapes are similar shapes.

The perimeter of quadrilateral WXYZ is 20cm

The given parameters are:

[tex]\mathbf{WX \cong DC}[/tex]

[tex]\mathbf{XY \cong BC}[/tex]

This means that, the perimeter of WXYZ is the same as the perimeter of BADC.

The perimeter of BADC is calculated using:

[tex]\mathbf{P_{BADC} = 2(AD + AB)}[/tex]

Substitute values for AD and AB

[tex]\mathbf{P_{BADC} = 2(4 + 6)}[/tex]

[tex]\mathbf{P_{BADC} = 2(10)}[/tex]

[tex]\mathbf{P_{BADC} = 20}[/tex]

Recall that both shapes are congruent, and they have the same perimeter.

This means that:

[tex]\mathbf{P_{WXYZ} = 20}[/tex]

Hence, the perimeter of quadrilateral WXYZ is 20cm