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MATH / Each of △PQR and △STU has an area of 1. In △PQR, U, W, and V are the midpoints of the sides. In △STU, R, V, and W are the midpoints of the sides. What is the area of parallelogram …

Problem

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problem

Each of △PQR\triangle PQR and △STU\triangle STU has an area of 1.1. In △PQR,\triangle PQR, U,U, W,W, and VV are the midpoints of the sides. In △STU,\triangle STU, R,R, V,V, and WW are the midpoints of the sides. What is the area of parallelogram $UVRW?$ [asy] draw((0,0)--(2,0)--(1,2)--cycle,linewidth(1)); draw((0,2)--(2,2)--(1,0)--cycle,linewidth(1)); label("TT",(0,0),SW); label("RR",(1,0),S); label("SS",(2,0),SE); label("WW",(1.5,1),E); label("QQ",(2,2),NE); label("UU",(1,2),N); label("PP",(0,2),NW); label("VV",(0.5,1),W); [/asy]
Plain-text mathematical notation (without MathML)
Each of △PQR and △STU has an area of 1. In △PQR, U, W, and V are the midpoints of the sides. In △STU, R, V, and W are the midpoints of the sides. What is the area of parallelogram $UVRW?$ [asy]
draw((0,0)--(2,0)--(1,2)--cycle,linewidth(1));
draw((0,2)--(2,2)--(1,0)--cycle,linewidth(1));
label("T",(0,0),SW);
label("R",(1,0),S);
label("S",(2,0),SE);
label("W",(1.5,1),E);
label("Q",(2,2),NE);
label("U",(1,2),N);
label("P",(0,2),NW);
label("V",(0.5,1),W);
[/asy]
Original LaTeX notation
Each of $\triangle PQR$ and $\triangle STU$ has an area of $1.$ In $\triangle PQR,$ $U,$ $W,$ and $V$ are the midpoints of the sides. In $\triangle STU,$ $R,$ $V,$ and $W$ are the midpoints of the sides. What is the area of parallelogram $UVRW?$ [asy]
draw((0,0)--(2,0)--(1,2)--cycle,linewidth(1));
draw((0,2)--(2,2)--(1,0)--cycle,linewidth(1));
label("$T$",(0,0),SW);
label("$R$",(1,0),S);
label("$S$",(2,0),SE);
label("$W$",(1.5,1),E);
label("$Q$",(2,2),NE);
label("$U$",(1,2),N);
label("$P$",(0,2),NW);
label("$V$",(0.5,1),W);
[/asy]

level

Level 3

type

Geometry

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Source and history

task_id
124da209-cd40-5d79-9f2c-372fbf49ef55
task_key
geometry--test--124da209-cd40-5d79-9f2c-372fbf49ef55
task_revision_id
1
config / split
geometry / test

Official source

initial import