<prompt> Pembetatu iliyo sawa ABC ina urefu wa upande sqrt111. Kuna pembetatu nne tofauti AD_1E_1, AD_1E_2, AD_2E_3, na AD_2E_4, kila mshikamano na pembetatu ABC, na BD_1 BD_2 sqrt11. Tafuta sum_k14CE_k2.  <response>: Pembetatu nne zinazolingana na pembetatu ABC zimeonyeshwa hapa chini.asyukubwa wa kitengo sentimita 0.4;jozi A, B, C, trans;jozi D, E;A 0,0;B sqrt111,0;C sqrt111dir60;D1 sehemu ya makutanoMduaraB,sqrt11,arcA,sqrt111,0,90;E1 zungusha60D1;E2 zungusha-60D1;kuchoraA--B--C--mzunguko;kuchoraA--D1--E1--mzunguko;kuchoraA--E2--D1;choraMduaraB,sqrt11, umekatika;kuchoraB--D1;kuchoraC--E1;kuchoraC--E2;leboA, A, SW;leboB, B, SE;leboC, C, NE;leboD_1, D1, NE;leboE_1, E1, N;leboE_2, E2, S;D2 sehemu ya makutanoMduaraB,sqrt11,arcA,sqrt111,0,-90;E3 zungusha60D2;E4 zungusha-60D2;trans 18,0;kuchorakuhamatransA--B--C--mzunguko;kuchorakuhamatransA--D2--E3--mzunguko;kuchorakuhamatransA--E4--D2;choraMduaraB trans,sqrt11, umekatika;kuchorakuhamatransB--D2;kuchorakuhamatransC--E3;kuchorakuhamatransC--E4;leboA, A trans, SW;leboB, B trans, dir0;leboC, C trans, N;leboD_2, D2 trans, SE;leboE_3, E3 trans, NE;leboE_4, E4 trans, S;asyKwa muunganisho wa SSS, pembetatu BAD_1 na BAD_2 zinalingana, kwa hivyo angle BAD_1 pembe BAD_2. Acha theta angle BAD_1 angle BAD_2. Let s sqrt111 na r sqrt11.Kwa Sheria ya Cosine kwenye pembetatu ACE_1,r2 CE_12 2s2 - 2s2 cos theta.Kwa Sheria ya Cosines kwenye pembetatu ACE_2,anzaalignCE_22 2s2 - 2s2 cos 120circ - theta 2s2 - 2s2 cos 240circ theta.endalignKwa Sheria ya Cosines kwenye pembetatu ACE_3,CE_32 2s2 - 2s2 cos theta.Kwa Sheria ya Cosines kwenye pembetatu ACE_4,CE_22 2s2 - 2s2 cos 120circ theta.Kumbuka kwambaanzaaligncos theta cos 120circ theta cos 240circ theta cos theta cos 120circ cos theta - sin 120 circ dhambi theta cos 240circ cos theta - dhambi 240zingira dhambi theta cos theta - frac12 cos theta - fracsqrt32 sin theta - frac12 cos theta fracsqrt32 sin theta 0,mwishoalignhivyoanzaalignCE_12 CE_22 CE_32 CE_42 2s2 - 2s2 cos theta 2s2 - 2s2 cos 240circ theta quad 2s2 - 2s2 cos theta 2s2 - 2s2 cos 120circ theta 8s2 - 2s2 cos theta.mwishoalignTangu 2s2 cos2 theta 2s2 - r2,8s2 - 2s2 cos theta 8s2 - 2s2 - r2 r2 6s2 677. 