.
9 82 . 15 . .
.
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
.
S = ah
S = BC * BK
S = 11 * 9 = 99
: 99 2.
. , =8, =6 =4.
.
DK.
, AOB DKC, COB AKD . , - , , .
, .
S = 2SAOB +2SBOC
.
S = 2 (1/2 8 * 4) + 2 (1/2 6 * 4) = 56 2
: 56 2.
. ( ). , - .
. : .
.
5 . . 30 . , , , . | 5 . . 30 . , , . |
.
, , AE=ED, ABE DBE ( : , AE=ED BE - , BE AD 90 ). , ADB 30 . , DBC 30 BC AD.
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ABE , ABE 180 - 90 - 30 = 60 . ( ABE DBE) EBD 60 . , ABD = 60 + 60 = 120 . BDC = ABD = 120 .
.
BE / BD = cos ∠EBD
BE / BD = cos 60
60 :
BE / BD = 1/2
BE = 5 ,
5 / BD = 1/2
BD = 10
: 10 , , 30 120 .