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MATH / A rectangular piece of paper ABCD is folded so that edge CD lies along edge AD, making a crease DP. It is unfolded, and then folded again so that edge AB lies along edge AD, making…
Problem
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problem
A rectangular piece of paper is folded so that edge lies along edge making a crease It is unfolded, and then folded again so that edge lies along edge making a second crease The two creases meet at forming triangles and . If and what is the area of quadrilateral in
$\mbox{cm}^2?$
[asy]
size(250);
draw((0,0)--(5,0)--(5,8)--(0,8)--cycle,black+linewidth(1));
draw((8,0)--(8,8)--(13,8)--(13,5)--(8,5),black+linewidth(1));
draw((8,0)--(13,5),black+linewidth(1)+dashed);
draw((16,0)--(21,0)--(21,8)--(16,8)--cycle,black+linewidth(1));
draw((16,0)--(21,5),black+linewidth(1)+dashed);
draw((16,8)--(21,3),black+linewidth(1)+dashed);
draw((12,0)--(10,2),black+linewidth(1));
draw((12,0)--(10,2),EndArrow);
label("",(0,8),N);
label("",(5,8),N);
label("",(5,0),S);
label("",(0,0),S);
label("",(8,8),N);
label("",(13,8),N);
label("",(8,5),W);
label("",(8,0),S);
label("",(13,5),E);
label("",(16,8),N);
label("",(21,8),N);
label("",(21,0),S);
label("",(16,0),S);
label("",(21,5),E);
label("",(21,3),E);
label("",(20,4),W);
[/asy]Plain-text mathematical notation (without MathML)
A rectangular piece of paper ABCD is folded so that edge CD lies along edge AD, making a crease DP. It is unfolded, and then folded again so that edge AB lies along edge AD, making a second crease AQ. The two creases meet at R, forming triangles PQR and ADR. If AB=5 cm and AD=8 cm, what is the area of quadrilateral DRQC, in $\mbox{cm}^2?$
[asy]
size(250);
draw((0,0)--(5,0)--(5,8)--(0,8)--cycle,black+linewidth(1));
draw((8,0)--(8,8)--(13,8)--(13,5)--(8,5),black+linewidth(1));
draw((8,0)--(13,5),black+linewidth(1)+dashed);
draw((16,0)--(21,0)--(21,8)--(16,8)--cycle,black+linewidth(1));
draw((16,0)--(21,5),black+linewidth(1)+dashed);
draw((16,8)--(21,3),black+linewidth(1)+dashed);
draw((12,0)--(10,2),black+linewidth(1));
draw((12,0)--(10,2),EndArrow);
label("A",(0,8),N);
label("B",(5,8),N);
label("C",(5,0),S);
label("D",(0,0),S);
label("A",(8,8),N);
label("B",(13,8),N);
label("C",(8,5),W);
label("D",(8,0),S);
label("P",(13,5),E);
label("A",(16,8),N);
label("B",(21,8),N);
label("C",(21,0),S);
label("D",(16,0),S);
label("P",(21,5),E);
label("Q",(21,3),E);
label("R",(20,4),W);
[/asy]Original LaTeX notation
A rectangular piece of paper $ABCD$ is folded so that edge $CD$ lies along edge $AD,$ making a crease $DP.$ It is unfolded, and then folded again so that edge $AB$ lies along edge $AD,$ making a second crease $AQ.$ The two creases meet at $R,$ forming triangles $PQR$ and $ADR$. If $AB=5\mbox{ cm}$ and $AD=8\mbox{ cm},$ what is the area of quadrilateral $DRQC,$ in $\mbox{cm}^2?$
[asy]
size(250);
draw((0,0)--(5,0)--(5,8)--(0,8)--cycle,black+linewidth(1));
draw((8,0)--(8,8)--(13,8)--(13,5)--(8,5),black+linewidth(1));
draw((8,0)--(13,5),black+linewidth(1)+dashed);
draw((16,0)--(21,0)--(21,8)--(16,8)--cycle,black+linewidth(1));
draw((16,0)--(21,5),black+linewidth(1)+dashed);
draw((16,8)--(21,3),black+linewidth(1)+dashed);
draw((12,0)--(10,2),black+linewidth(1));
draw((12,0)--(10,2),EndArrow);
label("$A$",(0,8),N);
label("$B$",(5,8),N);
label("$C$",(5,0),S);
label("$D$",(0,0),S);
label("$A$",(8,8),N);
label("$B$",(13,8),N);
label("$C$",(8,5),W);
label("$D$",(8,0),S);
label("$P$",(13,5),E);
label("$A$",(16,8),N);
label("$B$",(21,8),N);
label("$C$",(21,0),S);
label("$D$",(16,0),S);
label("$P$",(21,5),E);
label("$Q$",(21,3),E);
label("$R$",(20,4),W);
[/asy]level
Level 5
type
Geometry
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