. , - . " " sqrt(), sqrt - , . "√".
.
, 16 3 2 (16√3). .
.
- . , .
:
:
16√3 = a2 √3 / 4
16 = a2 / 4
a2 = 64
a = 8
() . ,
8 * 3 = 24
: 24 .
.
10 , 16 . .
.
, AO .
( )
,
:
AM2 = MO2 + AO2
(10 ), AO = 16√3/3
AM2 = 100 + 256/3
AM = √(556/3)
.
S = 1/2 * 16 sqrt((√(556/3) + 8) (√(556/3) - 8))
S = 8 sqrt((556/3) - 64)
S = 8 sqrt(364/3)
S = 16 sqrt(91/3)
,
3S = 48 √(91/3)
: 48 √(91/3)
( 2)
. , - . " " sqrt(), sqrt - , . "√".
60 . 2√3. .
.
. . :
S = 3√3 r2 = 3√3 (2√3)2 = 36√3
60 , MOK
|
|
|
tg MKO = MO/KO
tg 60 = MO / (2√3)
tg 60 = √3
√3 = MO / (2√3)
MO = 6
, 6 .
:
S = 1/3 Sh
S = 1/3 * 36√3 * 6
S = 72√3
: 72√3
3 45 . .
.
, .
So = 9 * √3/4
, , KM. OKM 45 .
:
OK / MK = cos 45
.
OK / MK = √2/2
, O .
( )
OK = √3/6 a
OK = √3/6 * 3 = √3/2
OK / MK = √2/2
√3/2 / MK = √2/2
MK = √3/√2
.
S = 1/2 * 3√(3/2)
S = 9√3/4 + 3/2 √(3/2)
( 3)
. , - . " " sqrt(), sqrt - , . "√".
.
3 . 45 .
.
.
:
, .
h = √3/2 a
a = h / (√3/2)
a = 3 / (√3/2)
a = 6 / √3
:
S = √3/4 a2
S = √3/4 (6 / √3)2
S = 3√3
, , KM. OKM 45 .
:
OK / MK = cos 45
.
OK / MK = √2/2
, O .
OK = √3/6 a
OK = √3/6 * 6/√3 = 1
OK / MK = √2/2
1 / MK = √2/2
MK = 2/√2
.
S = 1/2 (6 / √3) (2/√2) = 6/√6
,
S = 3√3 + 3 * 6/√6
S = 3√3 + 18/√6
: 3√3 + 18/√6
( 4)
. , - . " " sqrt(), sqrt - , . "√".
|
|
|
.
4 , 8 .
.
.
, MK = 8, MO = 4, OKM
MO/MK = 1/2
arcsin 1/2 = 30 .
KO / MK = cos 30
KO / 8 = cos 30
KO = 8 cos 30
30 .
KO = 8√3/2 = 4√3
, KO ( ).
r = a√3/6
,
4√3 = a√3/6
a = 24
, , :
S = 1/2 * 24 * 8 = 96 2
S = 3 S = 3 * 96 = 288 2.
: 288 2.
()
. ( , ). , - . " " sqrt(), sqrt - , . "√".
( . " ")
- .
4 , 4 6 .
.
:
S -
V -
h - ,
r -
R -
a -
