The perimeter of trapezoid WXYZ, to the nearest hundredth, is: 195.00 units.
What is the Perimeter of a Shape?
Perimeter of a shape is the sum of all the sides of the shape.
Perimeter of trapezoid WXYZ = WX + XY + YZ + ZW
Find XY and ZW.
Since △VXY and △VWZ are similar triangles, therefore:
VY/VZ = VX/VW
VY = 80
VZ = 80 - 50 = 30
VX = 62.5 + VW
VW = ?
Substitute
80/30 = (62.5 + VW)/VW
Cross multiply
80VW = 30(62.5 + VW)
80VW = 1,875 + 30VW
80VW - 30VW = 1,875
50VW = 1,875
VW = 1,875/50
VW = 37.5
Using Pythagorean theorem, find ZW:
ZW = √(VW² - VZ²)
Substitute
ZW = √(37.5² - 30²)
ZW = 22.5
Find XY:
XY/ZW = VY/VZ
XY/22.5 = 80/30
XY = (80 × 22.5)/30
XY = 60
Perimeter of trapezoid WXYZ = WX + XY + YZ + ZW
= 62.5 + 60 + 50 + 22.5
= 195.00 units.
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