<prompt> Vipeo vya pentagoni mbonyeo ni -1, -1, -3, 4, 1, 7, 6, 5 na 3, -1. Eneo la pentagon ni nini? asykuagiza grafu; ukubwa 150; halisi lsf0.5; pen dpslinewidth0.7fontsize10; defaultpendps; kalamu dsnyeusi; xmin halisi-4.5,xmax7.5,ymin-2.5,ymax8.5;kalamu zzzrgb0.6,0.6,0.6;gridi kalamu gslinewidth0.7zzz; gx1,gy1 halisi;kwaiceil halisixmingxgx;isakafuxmaxgxgx;igx chorai,ymin--i,ymax,gs; kwareal iceilymingygy;ifloorymaxgygy;igy drawxmin,i--xmax,i,gs;Laxis ya lebo; laxis.pfontsize10; kamba tupux halisireturn ;xaxisxmin,xmax,defaultpenzzzlinewidth1.2,juukweli; yaxisymin,ymax,defaultpenzzzlinewidth1.2,juukweli; chora-1,-1--3,-1; chora3,-1--6,5; chora1,7--6,5; chora-1,-1---3,4; chora-3,4--1,7;nukta -1,-1, ds; nukta -3,4, ds; nukta 6,5, ds; nukta 3,-1, ds; nukta 1,7, ds;klipuxmin,ymin--xmin,ymax--xmax,ymax--xmax,ymin--mzunguko;asy  <response>: Chora mstatili wenye vipeo -3,7,-3,-1,6,-1,6,7 kuhusu pentagoni, kama inavyoonyeshwa hapa chini: asykuagiza grafu; ukubwa 4.45cm; halisi lsf0.5; pen dpslinewidth0.7fontsize10; defaultpendps; kalamu dsnyeusi; xmin halisi-4.5,xmax7.5,ymin-2.5,ymax8.5;kalamu zzzrgb0.6,0.6,0.6;gridi kalamu gslinewidth0.7zzz; gx1,gy1 halisi;kwaiceil halisixmingxgx;isakafuxmaxgxgx;igx chorai,ymin--i,ymax,gs; kwareal iceilymingygy;ifloorymaxgygy;igy drawxmin,i--xmax,i,gs;Laxis ya lebo; laxis.pfontsize10; kamba tupux halisireturn ;xaxisxmin,xmax,defaultpenzzzlinewidth1.2,juukweli; yaxisymin,ymax,defaultpenzzzlinewidth1.2,juukweli; chora-1,-1--3,-1; chora3,-1--6,5; chora1,7--6,5; chora-1,-1---3,4; chora-3,4--1,7; chora-3,7---3,-1--6,-1--6,7--mzunguko,upana wa mstari1.4;nukta -1,-1, ds; nukta -3,4, ds; nukta 6,5, ds; nukta 3,-1, ds; nukta 1,7, ds;kalamu sm fontsize12;leboA_2,-3,7,SE,sm; leboA_3,-3,-1,NE,sm; leboA_4,6,-1,NW,sm; leboA_1,6,7,SW,sm;klipuxmin,ymin--xmin,ymax--xmax,ymax--xmax,ymin--mzunguko;asy Eneo la pentagoni ni tofauti kati ya eneo la mstatili na pembetatu nne za kulia zinazoundwa kwenye vipeo vya mstatili. Tunapata kwamba anzaalignA_1 frac 12 cdoti 5 cdoti 2 5, A_2 frac 12 cdoti 4 cdoti 3 6, A_3 frac 12 cdot 2 cdot 5 5, A_4 frac 12 cdoti 3 cdoti 6 9,mwishoalign ilhali eneo la mstatili mzima ni 9 mara 8 72. Kwa hivyo, eneo la pentagon ni sawa na 72 -5 - 6 -5 - 9 47 vitengo vya mraba. 