In parallelogram
shown above,
is the midpoint of
,
is the midpoint of
.
is a point on
such that ratio
equal
. If the area of this parallelogram is 776, find Area of triangle
.
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A r e a A B E = A F D = 2 F E C = 1 / 4 ∗ A B C D . A r e a A E F = A r e a s A B C D − ( A B E + A F D + F E C = 3 / 8 ∗ A B C D A r e a A E G = 1 / 3 ∗ A E F = 1 / 8 ∗ A B C D = 7 7 6 / 8 = 9 7 .
D e t a i l s : − A r e a ∣ ∣ g r a m A B C D = B C ∗ H e i g h t . A r e a Δ A B E = 2 1 ∗ 2 B C ∗ H e i g h t = 7 7 6 / 4 . A r e a Δ A F D = 2 1 ∗ 2 H e i g h t ∗ A D = 2 1 ∗ 2 H e i g h t ∗ B C = 7 7 6 / 4 . A r e a Δ D E C = 2 1 ∗ 2 B C ∗ H e i g h t = 7 7 6 / 4 . B u t A r e a Δ F E C = 2 1 ∗ A r e a Δ D E C = 7 7 6 / 8 . B a s e i s 1 / 2 . S o A r e a Δ A E F = ( 1 − 1 / 4 − 1 / 4 − 1 / 8 ) ∗ 7 7 6 . B u t A r e a Δ A E G = 3 1 Δ A E F = 3 1 ∗ 8 3 ∗ 7 7 6 = 9 7 . B a s e i s 1 / 3 .