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2019 ASDAN Math Tournament
5
5
Part of
2019 ASDAN Math Tournament
Problems
(1)
2019 Geometry # 5
Source:
9/10/2023
Trapezoid
A
B
C
D
ABCD
A
BC
D
has properties
A
B
∥
C
D
AB \parallel CD
A
B
∥
C
D
,
A
B
=
15
AB = 15
A
B
=
15
,
C
D
=
27
CD = 27
C
D
=
27
, and
B
C
=
A
D
=
10
BC = AD = 10
BC
=
A
D
=
10
. A smaller trapezoid
E
F
G
H
EF GH
EFG
H
is drawn within
A
B
C
D
ABCD
A
BC
D
with
A
B
∥
E
F
AB\parallel EF
A
B
∥
EF
,
B
C
∥
F
G
BC\parallel F G
BC
∥
FG
,
C
D
∥
G
H
CD\parallel GH
C
D
∥
G
H
, and
D
A
∥
H
E
DA\parallel HE
D
A
∥
H
E
such that each edge in
A
B
C
D
ABCD
A
BC
D
is a distance
2
2
2
away from the corresponding edge in
E
F
G
H
EF GH
EFG
H
. Compute the area of
E
F
G
H
EF GH
EFG
H
.
geometry
2019