.
- . S = a2√3.
S = 3√3
: 3√3
.
4 .
.
, ,
AO = R = √3 / 3 a
AO = 4√3 / 3
, OM AOM
AO2 + OM2 = AM2
OM2 = AM2 - AO2
OM2 = 42 - (4√3 / 3)2
OM2 = 16 - 16/3
OM = √(32/3)
OM = 4√2 / √3
V = 1/3 Sh
S = √3/4 a2
V = 1/3 (√3 / 4 * 16) (4√2 / √3)
V = 16√2 / 3
: 16√2 / 3
. ( ). , - . " " sqrt(), sqrt - , .
ABCD 5 , BD 6 . , , OK, . (, , , D) = 8.
.
, , , . , .
, BO BD.
BO = BD / 2 = 6 / 2 = 3
OK , BOK . , BK.
BK2 = BO2 + OK2
BK2 = 32 + 82
BK2 =73
BK = sqrt (73), 73
BKO DKO (KO - , BO=OD , ), BK = BD.
AK. , , , :
AB2 = BO2 + AO2
52 = 32 + AO2
AO2 = 52 - 32
AO2 = 16
AO = 4
AK
AK2 = AO2 + OK2
BK2 = 42 + 82
BK2 = 80
BK = 4 sqrt(5),
AOK COK , AO = CO.
: AO CO , BO DO 73
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4. 45 . .
.
, 45 , . - S = 1/2 Pa, P - , a - . , . - .
, 180 , , 180 - 90 - 45 = 45. - .
, ( , , , ).
, , , ,
a = sqrt(42 + 42) = sqrt(32) = 4 sqrt(2),
4 * 2 * 4 = 32 ,
S = 1/2 Pa = 1 / 2 * 32 * 4 sqrt(2) = 64 sqrt(2), 64
: 64
24 , 26 . : ) ) ) .
.
, , . :
S = 1/4 sqrt((a + b + c)(b + c - a)(a + c - b)(a + b -c))
S = 1/4 sqrt((26 + 26 + 24)(26 + 24 - 26)(26 + 24 - 26)(26 + 26 - 24))
S = 1/4 sqrt(76 * 24 * 24 * 28) = 1/4 sqrt(1225728) ≈ 276, 78 2.
, . ,
2 + 2 = 242
22 = 576
2 = 288
= sqrt(288) ≈ 16.97
,
S = 1/4 sqrt((a + b + c)(b + c - a)(a + c - b)(a + b -c))
S = 1/4 sqrt((26 + 26 + sqrt(288))(26 + sqrt(288) -26)(26 + sqrt(288) -26)(26 + 26 - sqrt(288)))
S = 1/4 sqrt(695808) ≈ 208.54 2.
4S = sqrt(695808) ≈ 208.54 2.
: 1/4 sqrt(1225728) 2, sqrt(288) , sqrt(695808) 2.