<prompt> Mchemraba ABCDEFGH, ulioandikwa kama inavyoonyeshwa hapa chini, una urefu wa ukingo 1 na hukatwa na ndege inayopita kwenye kipeo D na sehemu za kati M na N ya overlineAB na overline CG mtawalia. Ndege hugawanya mchemraba katika mango mbili. Pata kiasi cha kubwa ya yabisi mbili.asykuagiza cse5;ukubwa wa kitengo 8mm;njianyeusi;jozi A 0,0, B 3.8,0, C 5.876,1.564, D 2.076,1.564, E 0,3.8, F 3.8,3.8, G 5.876,5.364, H 2.076,5.364, M 1.9,0, N 5.876,3.465;jozi yenye nukta A,B,C,D,E,F,G,H,M,N;DA--B--C--G--H--E--A;DE--F--B;DF--G;pathpendashed;DA--D--H;DD--C;nukta nukta;leboA,A,SW;leboB,B,S;leboC,C,SE;leboD,D,NW;leboE,E,W;leboF,F,SE;leboG,G,NE;leboH,H,NW;leboM,M,S;leboN,N,NE;asy  <response>: Bainisha mfumo wa kuratibu wenye D ilipo asili na C,A, na H kwenye x-, y-, na z-axes mtawalia. Kisha D0,0,0, Mleftfrac12,1,0kulia, na Nleft1,0,frac 12kulia. Ndege inayopitia D,M, na N ina mlinganyo2x-y-4z0.Ndege hii inakatiza overlineBF at Q left1,1,frac14right. Let P 1,2,0. Kwa kuwa 21 - 12 - 40 0, P iko kwenye ndege. Pia, P iko kwenye viendelezi vya sehemu overlineDM, overlineNQ, na overlineCB.asykuagiza cse5;ukubwa wa kitengo 8mm;njianyeusi;jozi A 0,0, B 3.8,0, C 5.876,1.564, D 2.076,1.564, E 0,3.8, F 3.8,3.8, G 5.876,5.364, H 2.076,5.364, M 1.9,0, N 5.876,3.465;jozi Q interpB,F,14, P 2B - C;jozi yenye nukta A,B,C,D,E,F,G,H,M,N,P,Q;DA--B--C--G--H--E--A;DE--F--B;DF--G;pathpendashed;DA--D--H;DD--C;nukta nukta;leboA,A,SW;leboB,B,S;leboC,C,SE;leboD,D,NW;leboE,E,W;leboF,F,SE;leboG,G,NE;leboH,H,NW;leboM,M,SW;leboN,N,dir0;leboP,P,S;leboQ,Q,NW;choraM--D--N,dashed;choraM--P--N;choraP--B;kuchoraM--Q;asyKisha tunaweza kuoza piramidi PCDN kuwa piramidi PBMQ na frustum BMQCDN. Piramidi PCDN ina msingi wa 1 na urefu wa frac12, kwa hivyo ujazo wake ni PCDN frac16. Kumbuka kuwa piramidi PBMQ ni sawa na piramidi PCDN, yenye kufanana frac12, hivyoPBMQ kushoto frac12 kulia3 cdot frac16 frac148.KishaBMQCDN frac16 - frac148 frac748,kwa hivyo ujazo wa ile ngumu zaidi, iliyokatwa kwa ndege DMQN, ni 1 - frac748 frac4148. 