Find the shaded area
∠
A
=
∠
A
C
B
=
∠
A
B
C
,
G
J
=
J
F
,
D
I
=
I
F
,
H
C
=
C
F
=
F
B
=
B
E
,
G
H
=
D
E
=
8
cm
,
A
C
=
1
2
cm
,
area
(
J
C
F
)
=
4
1
area
(
G
H
F
)
,
area
(
I
B
F
)
=
4
1
area
(
D
E
F
)
.
Find the shaded area up to 3 decimal places.
The answer is 41.569.
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2 solutions
A F i s t h e l i n e o f s y m m e t r y . . . . . . . . . . ( 1 ) A F i s a l t i t u d e o f e q u i l a t e r a l Δ A C B . ⟹ B F = 2 1 B C = 6 . . . . . . . . . . ( 2 ) A l s o Δ A C B = 4 3 ∗ 1 2 2 = 3 6 ∗ 3 . . . . . . . . . . . . . ( 3 ) I n Δ F G H , J a n d C a r e m i d p o i n t s o f t h e s i d e s . ∴ J C = 2 1 G H = 4 . S o b y ( 1 ) a r e a o f Δ s I F B = J C F = 2 1 ∗ H G ∗ B F ∗ S i n 6 0 = 6 ∗ 3 . ∴ A r e a s A J F I = Δ A B C − Δ J C F − Δ I F B = 2 4 ∗ 3 = 4 1 . 5 6 9 .