<prompt> Mche hutengenezwa ili kingo zake za wima zilingane na mhimili wa z. Sehemu yake ya msalaba ni mraba wa urefu wa upande 10.asykuagiza tatu;ukubwa 180;makadirio ya sasa mtazamo 6,3,2;mara tatu A, B, C, D, E, F, G, H;A 1,1,0;B 1,-1,0;C -1,-1,0;D -1,1,0;E A 0,0,1;F B 0,0,3;G C 0,0,4;H D 0,0,2;kuchorausoE--F--G--H--mzunguko,kijivu0.7,nolight;kuchoraE--F--G--H--mzunguko;kuchoraA--E;choraB--F;kuchoraC--G,dashed;kuchoraD--H;kuchoraB--A--D;kuchoraB--C--D,dashed;asyKisha prism hukatwa na ndege 4x - 7y 4z 25. Pata eneo la juu la sehemu ya msalaba.  <response>: Tunaweza kudhani kuwa msingi wa mraba umejikita katika 0,0,0. Wima zote za msingi ziko kwenye mduara wenye radius frac10sqrt2 5 sqrt 2, kwa hivyo tunaweza kudhani kuwa wima za msingi nianzaalignA 5 sqrt2 cos theta, 5 sqrt2 sin theta, B -5 sqrt2 sin theta, 5 sqrt2 cos theta, C -5 sqrt2 cos theta, -5 sqrt2 sin theta, D 5 sqrt2 sin theta, -5 sqrt2 cos theta.endalignVipeo vya kata viko kwenyeanzaalignE kushoto 5 sqrt2 cos theta, 5 sqrt2 sin theta, frac35 sqrt2 sin theta - 20 sqrt2 cos theta 254 kulia, F kushoto -5 sqrt2 sin theta, 5 sqrt2 cos theta, frac35 sqrt2 cos theta 20 sqrt2 dhambi theta 254 kulia, G kushoto -5 sqrt2 cos theta, -5 sqrt2 sin theta, frac-35 sqrt2 sin theta 20 sqrt2 cos theta 254 kulia, H kushoto 5 sqrt2 sin theta, -5 sqrt2 cos theta, frac-35 sqrt2 cos theta - 20 sqrt2 sin theta 254 kulia.endalignKumbuka kwamba EFGH ya pembe nne ni msambamba. Katikati ya parallelogram niM left 0, 0, frac254 kulia.Eneo la pembetatu EMF kisha hutolewa na frac12 overrightarrow ME times overrightarrowMF. Tuna hiyoanzaalignoverrightarrowME times overrightarrowMF left 5 sqrt2 cos theta, 5 sqrt2 sin theta, frac35 sqrt2 sin theta - 20 sqrt2 cos theta4 kulia mara kushoto -5 sqrt2 sin theta, 5 sqrt2 cos theta, frac 35 sqrt2 cos theta 20 sqrt2 sin theta4 kulia kushoto 50 cos2 theta 50 sin2 theta, -frac1752 cos2 theta - frac1752 sin2 theta, 50 cos2 theta 50 sin2 theta kulia kushoto 50, -frac1752, 50 kulia,endalignili eneo la pembetatu EMF liwefrac12 kushoto kushoto 50, -frac1752, 50 kulia kulia frac2254.Kwa hivyo, eneo la sambamba EFGH ni 4 cdot frac2254 225. Hasa, eneo la mkato wa sayari halitegemei mwelekeo wa prism. 