()
.
, 30 .
.
:
n- 180(n-2).
, () :
180 (4 - 2) = 360 .
, , . 30 , :
+ ( + 30) + + ( + 30) = 360
4 + 60 = 360
= 75
: () 75 105 .
.
, 30 .
.
:
. ( ). , - . √ sqrt(), .
() 8 20 . 10 . , , 12 .
.
B ABCD BM AD. C AD CN. MBCN ,
AD = BC + AM + ND
, , - . ,
AD = BC + AM * 2
AM = (AD - BC) / 2
AM = (20 - 8) / 2 = 6
, ABM, , . , , :
BM2 = AB2 - AM2
BM2 = 102 - 62
BM = 8
ABCD 8 , - 12 ,
k = 12 / 8 = 1,5
, . :
S = (AD * k + BC * k) / 2 * (BM * k)
S = (20 * 1,5 + 8 * 1,5) / 2 * (8 * 1,5) = (30 + 12) / 2 * 12 = 252 2
: 252 2
36, 25, 29. .
.
B ABCD BM AD. ABM BMD :
AB2 = BM2 + AM2
AD2 = BM2 + MD2
BM2 = AB2 - AM2
BM2 = AD2 - MD2
|
|
,
AB2 - AM2 = AD2 - MD2
252 - AM2 = 292 - MD2
AD = AM + MD,
AM + MD = 36
MD = 36 - AM
252 - AM2 = 292 - (36 -AM)2
625 - AM2 = 841 - (36 -AM)2
625 - AM2 = 841 - (1296 - 72AM + AM2)
625 - AM2 = 72AM - 455 - AM2
625 = 72AM - 455
AM = 15
MD = 36 - 15 = 21
AM = 15, 36 - 15 *2 = 6
:
BM2 = AB2 - AM2
BM2 = 625 - 225
BM = 20
.
S = 1/2 (36 + 6) * 20 = 420 2.
: 420 2.
( 2)
. ( ). , - . √ sqrt(), .
.
ABCD BC = 5 , ABC = 135 , 3 . .
.
B AD BE.
ABC ABE EBC. , EBC 90 . ABE = 135 - 90 = 45 .
BE - , ABE - . ABE, , EAB 180º - 90º - 45º = 45º. , ABE - , AE = BE = 3 .
ABCD - , 5 + 3 + 3 = 11 .
: 11 .
, , 5, 2 .
.
, ADB DBC, . , ADB BDC . , CBD CDB .
, BCD - . , 5 , BC 5 .
, , 10 .
. (5 + 10) / 2 = 7,5
: 7,5 .
a b . . , .
.
, , , () .
(1):
, - .
:
S = (2a + 2b) (a + b) / 2
S = (a + b)2
: S = (a + b)2.