. . , .
.
. , 7
.
:
a = 7
7h, h - , - ,
49√3 / 4 = 3 * 7h
49√3 / 4 = 21h
h = 7√3 / 12
: 7√3 / 12
.
h.
, , , .
.
, . , . .
AD = BC , BOC = AOD , BCO = OAD, OBC = ODA AD BC. BOC AOD .
, BO = OD, BOC COD , OC, COB = COD = 90 . , CD =BC = AD = AB.
ABCD -
,
V = Sh
- .
S = √3/4 h2
V = √3/4 h3
: √3/4 h3.
( 2)
. . , .
.
, 6 , - 10 .
.
:
a = 6 S = √3 / 4 * 36 = 9√3
,
9√3 * 2 = 18√3
6 * 10 = 60, , 60 * 3 = 180
, 180 + 18√3 ≈ 211, 18 .
: 180 + 18√3 ≈ 211,18
. ( ). , . , - .
7 8. 8/. .
.
, .
|
|
, , .
72 + 82 = 113
n- . : n- , ( ).
, , .
, , , , , , . , :
V= r2h,
-
r -
h -
, , , , 113 , , r2=113/4.
8/.
:
V=*113/4*8/
V=226
: 226
, 8. 12. - .
.
,
S = 2S1 + S2 + 2S3, S1 - , S2 - , , S3 - , . ( , , , )
, , , 12 . ( ).
, .
S1 = 1/2ah = 1/2 * 12 * 8 = 48 2.
, ( , 12 /2 = 6 , )
sqrt(62 + 82) = 10
S2 = 12 * 12 = 144 2.
S3 = 10 * 12 = 120 2.
S = 2S1 + S2 + 2S3 = 2 * 48 + 144 + 2 *120 = 480 2.
: 480 2.
( 2)
. ( , ). , - . " " sqrt(), sqrt - , . "√".
. , 7.
.
, , :
S = a2√3 / 4
S = 49√3 / 4
|
|
S = 3 ab
S = 3 * 7 * b = 21b
,
49√3 / 4 = 21b
b = 49√3 / 84
b = 7√3 / 12
: 7√3 / 12
8 6 . , 120 .
.
.
AB2 = AC2 + BC2
AB2 = 82 + 62
AB2 = 64 + 36
AB = √100
AB = 10
h. , . - ACC1A1, CBB1C1 ABB1A1 , ,
10h + 6h + 8h = 120
24h = 120
h =5
: 5 .
( 3)
. ( , ). , - . " " sqrt(), sqrt - , . "√".
.
- 5 3 120 . 35 2, .
.
AC2 = AB2 + BC2 - 2*AB*BC*cos 120
AC2 = 25 + 9 - 2*5*3*cos 120
120 .
AC2 = 34 - 30 (-0.5)
AC2 = 49
AC = 7
. . , , .
7 .
35 / 7 = 5
,
S = 5*5 + 3*5 + 7*5 = 75 2
: 75 2.