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9 82 . 15 . .

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ABCD, B AD BK.
ABK, , . :

AB2 = BK2 + AK2
82 = 92 + AK2
AK2 = 82 - 81
AK = 1

BC AN . AN = BK ANBK. ANC NC.
AN2 + NC2 = AC2
92 + NC2 = 152
NC2 = 225 - 81
NC2 = √144
NC = 12

BC ABCD.
BC = NC - NB
, NB = AK ,
BC = 12 - 1 = 11

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S = ah
S = BC * BK
S = 11 * 9 = 99

: 99 2.

. , =8, =6 =4.

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DK.
, AOB DKC, COB AKD . , - , , .

, .
S = 2SAOB +2SBOC

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S = 2 (1/2 8 * 4) + 2 (1/2 6 * 4) = 56 2
: 56 2.

. ( ). , - .
. : .

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5 . . 30 . , , , . 5 . . 30 . , , .

 

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, , AE=ED, ABE DBE ( : , AE=ED BE - , BE AD 90 ). , ADB 30 . , DBC 30 BC AD.

ABE , ABE 180 - 90 - 30 = 60 . ( ABE DBE) EBD 60 . , ABD = 60 + 60 = 120 . BDC = ABD = 120 .

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BE / BD = cos ∠EBD
BE / BD = cos 60
60 :
BE / BD = 1/2
BE = 5 ,
5 / BD = 1/2
BD = 10

: 10 , , 30 120 .





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