https://tex.z-dn.net/?f=S_%7BABD%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20AD%5Ccdot%20BD%5Ccdot%20%5Csin%7B%5Calpha%7D%5C%5C%5C%5CS_%7BCBD%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20CD%5Ccdot%20BD%5Ccdot%20%5Csin%7B(180%5E%7B%5Ccirc%7D-%5Calpha)%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20CD%5Ccdot%20BD%5Ccdot%20%5Csin%7B%5Calpha%7D%5C%5C%5C%5C%5Cfrac%7BS_%7BCBD%7D%7D%7BS_%7BABD%7D%7D%3D%5Cfrac%7B1%2F2%5Ccdot%20%5Ccdot%20CD%5Ccdot%20BD%5Ccdot%20%5Csin%7B%5Calpha%7D%7D%7B1%2F2%5Ccdot%20AD%5Ccdot%20BD%5Ccdot%20%5Csin%7B%5Calpha%7D%7D%3D%5Cfrac%7BCD%7D%7BAD%7D%3D%5Cfrac%7B13x%7D%7B2x%7D%5C%5C%5C%5CS_%7BCBD%7D%2BS_%7BABD%7D%3D75%3D15x%5CRightarrow%20x%3D5%5C%5C%5C%5CS_%7BABD%7D%3D2x%3D10%5C%5C%5C%5COtvet%5C!%5C!%3A%5C%3B10.
Объяснение:
https://tex.z-dn.net/?f=S_%7BABD%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20AD%5Ccdot%20BD%5Ccdot%20%5Csin%7B%5Calpha%7D%5C%5C%5C%5CS_%7BCBD%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20CD%5Ccdot%20BD%5Ccdot%20%5Csin%7B(180%5E%7B%5Ccirc%7D-%5Calpha)%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20CD%5Ccdot%20BD%5Ccdot%20%5Csin%7B%5Calpha%7D%5C%5C%5C%5C%5Cfrac%7BS_%7BCBD%7D%7D%7BS_%7BABD%7D%7D%3D%5Cfrac%7B1%2F2%5Ccdot%20%5Ccdot%20CD%5Ccdot%20BD%5Ccdot%20%5Csin%7B%5Calpha%7D%7D%7B1%2F2%5Ccdot%20AD%5Ccdot%20BD%5Ccdot%20%5Csin%7B%5Calpha%7D%7D%3D%5Cfrac%7BCD%7D%7BAD%7D%3D%5Cfrac%7B13x%7D%7B2x%7D%5C%5C%5C%5CS_%7BCBD%7D%2BS_%7BABD%7D%3D75%3D15x%5CRightarrow%20x%3D5%5C%5C%5C%5CS_%7BABD%7D%3D2x%3D10%5C%5C%5C%5COtvet%5C!%5C!%3A%5C%3B10.
Объяснение:
⇒ MC = 2*MD =2m и CD =MD + MC =m +2m =3m , AB =3*CD =3*3m=9m.
Очевидно: ΔANB ~ ΔCNM , причем коэффициент подобия
k =AB/ CM =9m/2m =9/2
ΔANB ~ ΔCNM ⇒ h₁/ h =k ⇒ h₁=k*h = 9h/2.
Высота трапеции ABCD равна : H = h+h₁=h +9h/2 =11h/2 .
S(CNM) =CM*h/2 =2m*h/2 =m*h ;
S(ABCD) =(AB +CD)/2 *H =(9m+3m)/2 * 11h/2 = 33m*h ;
S(CNM) / S(ABCD) =m*h /33m*h =1 : 33 .
* * * * * * * другой
Обозначаем S(CNM) = S , MD = m .
⇒ MC = 2*MD =2m и CD =MD + MC =m +2m =3m , AB =3*CD =3*3m=9m.
Очевидно: ΔANB ~ ΔCNM , причем коэффициент подобия
k =AN/CN = AB/ CM =9m/2m =9/2 .
Следовательно S(ANB) / S(CNM) = k² ⇒ S(ANB) = (81/4)*S .
S(ANM) / S(CNM) = AN / CN = 9/2 ⇒ S(AMN) = (9/2) *S .
S(BNC) = S(BCM) - S(CNM) = S(AMC) -S(CNM) =S(ANM) = (9/2) *S .
* * * т.е . треугольники BNC и ANM равновеликие * * *
S(AMC) = S(AMN) + S(CNM) = (9/2) *S +S =(11/2)*S .
S(ADM) / S(AMC) =MD / MC =1/2 ⇒ S(ADM) =(1/2)*(11/2) =(11/4)*S.
S(ABCD) =S(ADM) + S(AMCB)= S(ADM)+S(CNM) + S(ANB) +2*S(ANM) =
(11/4)*S + S +(81/4)*S+ 9*S =(92/4)*S+10*S = 33*S.
S / S(ABCD) = 1 : 33.
P.S. можно было использовать
S(ANM) *S(BCN) =S(CNM) * S(ANB) ⇔ S²(ANM)= 81S/4 *S;
S²(ANM) =9S/2 и т. д .