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2021 LMT Spring
B9
2021 Spring LMT Division B Problem 9
2021 Spring LMT Division B Problem 9
Source:
January 22, 2022
geometry
Problem Statement
Convex pentagon
P
Q
R
S
T
PQRST
PQRST
has
P
Q
=
T
P
=
5
PQ = T P = 5
PQ
=
TP
=
5
,
Q
R
=
R
S
=
S
T
=
6
QR = RS = ST = 6
QR
=
RS
=
ST
=
6
, and
∠
Q
R
S
=
∠
R
S
T
=
9
0
o
\angle QRS = \angle RST = 90^o
∠
QRS
=
∠
RST
=
9
0
o
. Given that points
U
U
U
and
V
V
V
exist such that
R
U
=
U
V
=
V
S
=
2
RU =UV = VS = 2
R
U
=
U
V
=
V
S
=
2
, find the area of pentagon
P
Q
U
V
T
PQUVT
PQ
U
V
T
.Proposed by Kira Tang
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