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MATH / In the diagram below, WXYZ is a trapezoid such that (WX)¯∥(ZY)¯ and (WY)¯⊥(ZY)¯. If YZ=12, tanZ=1.5, and tanX=3, then what is the area of WXYZ? [asy] pair WW,X,Y,Z; Z = (0,0); Y = …

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

In the diagram below, WXYZWXYZ is a trapezoid such that WX¯∥ZY¯\overline{WX}\parallel \overline{ZY} and WY¯⊥ZY¯\overline{WY}\perp\overline{ZY}. If YZ=12YZ = 12, tanZ=1.5\tan Z = 1.5, and tanX=3\tan X = 3, then what is the area of WXYZWXYZ? [asy] pair WW,X,Y,Z; Z = (0,0); Y = (12,0); WW = (12,18); X= (18,18); draw(WW--X--Y--Z--WW); label("WW",WW,N); label("XX",X,N); label("YY",Y,S); label("ZZ",Z,S); [/asy]
Plain-text mathematical notation (without MathML)
In the diagram below, WXYZ is a trapezoid such that (WX)¯∥(ZY)¯ and (WY)¯⊥(ZY)¯.  If YZ=12, tanZ=1.5, and tanX=3, then what is the area of WXYZ?

[asy]
pair WW,X,Y,Z;
Z = (0,0);
Y = (12,0);
WW = (12,18);
X= (18,18);
draw(WW--X--Y--Z--WW);
label("W",WW,N);
label("X",X,N);
label("Y",Y,S);
label("Z",Z,S);
[/asy]
Original LaTeX notation
In the diagram below, $WXYZ$ is a trapezoid such that $\overline{WX}\parallel \overline{ZY}$ and $\overline{WY}\perp\overline{ZY}$.  If $YZ = 12$, $\tan Z = 1.5$, and $\tan X = 3$, then what is the area of $WXYZ$?

[asy]
pair WW,X,Y,Z;
Z = (0,0);
Y = (12,0);
WW = (12,18);
X= (18,18);
draw(WW--X--Y--Z--WW);
label("$W$",WW,N);
label("$X$",X,N);
label("$Y$",Y,S);
label("$Z$",Z,S);
[/asy]

level

Level 4

type

Geometry

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Source and history

task_id
5dc3730e-067e-5825-bf5e-8f4088f1da56
task_key
geometry--test--5dc3730e-067e-5825-bf5e-8f4088f1da56
task_revision_id
1
config / split
geometry / test

Official source

initial import