Question

Find the perimeter of the trapezium WXYZ if WX = 7m, YZ = 13m and ZW = 8m.

• A. 32m
• B. 30m
• C. 39m
• D. 38m

Answer 1

The correct option is D 38m


Draw a line from point X parallel to ZW and perpendicular to the line ZY which meets ZY at M.
Therefore:
MY = ZY - ZM
MY = ZY - WX (as ZM = WX (opposite sides of a rectangle))
MY = 13 - 7
= 6m
XM = 8m ( XM = WZ opposite side of a rectangle)
Applying pythagoras theorem to the triangle XMY
$X{M}^2+M{Y}^2=X{Y}^2$
$X{Y}^2=8^2+6^2$
$XY=\sqrt{100}$
$XY=10m$
Therefore, perimeter of the trapezium
= WZ + ZY + XY + WX
= 8 + 13 + 10 + 7
= 38m