<prompt> Katika trapezoid ABCD na besi overlineAB na overlineCD, tuna AB 52, BC 12, CD 39, na DA 5. Eneo la ABCD ni nini?asyjozi A,B,C,D;A0,0;B4,0;C3.3,1;D0.3,1;leboA,A,S;leboB,B,S;leboC,C,N;leboD,D,N;lebo52,2,0,S;lebo39,1.8,1,N;lebo5,0.15,0.5,W;lebo12,3.65,0.5,E;kuchoraA--B--C--D--mzunguko;asy  <response>: Kushuka kwa mara ya kwanza perpendiculars kutoka D na C hadi overlineAB. Acha E na F ziwe miguu ya vigezo vya overlineAB kutoka D na C, mtawalia, na uruhusu h DE CF, quad x AE, quadtextnaquad y FB.asyjozi A,B,C,D;A0,0;B4,0;C3.3,1;D0.3,1;kuchoraD--0.3,0;kuchoraC--3.3,0;leboE,0.3,0,SE;leboF,3.3,0,S;lebox,0.15,0,S;leboy,3.65,0,S;leboh,0.3,0.5,E;leboh,3.3,0.5,W;leboA,A,SW;leboB,B,S;leboC,C,N;leboD,D,N;lebo39,2,0,S;lebo39,1.8,1,N;lebo5,0.15,0.5,W;lebo12,3.65,0.5,E;kuchoraA--B--C--D--mzunguko;asy Kisha 25 h2 x2, quad 144 h2 y2, quadtextnaquad 13 xy.Hivyo 144 h2 y2 h2 13-x2 h2 x2 169 - 26x 25 169- 26x,ambayo inatoa x 5026 2513, na h sqrt52 - kushotofrac2513kulia2 5sqrt1 - frac25169 5sqrtfrac144169 frac6013.Hivyo ni textEneo ABCD frac1239 52cdotfrac6013 210.maandishiORPanua overlineAD na overlineBC ili kukatiza kwa P. Kwa kuwa pembetatu PDC na pembetatu PAB zinafanana, tuna fracPDPD 5 frac3952 fracPCPC12.Hivyo PD 15 na PC 36. Kumbuka kuwa 15, 36 na 39 ni 5, 12 na 13 mtawalia, kwa hivyo angle APB ni pembe ya kulia. Eneo la trapezoid ni tofauti ya maeneo ya pembetatu PAB na pembetatu PDC, hivyo textEneoABCD frac122048 - frac121536 210.asyjozi A,B,C,D;A0,0;B4,0;C3.3,1;D0.3,1;leboA,A,S;leboB,B,S;leboC,C,E;leboD,D,W;kuchora1.2,4--C--D--mzunguko;leboP,1.2,4,N;kuchoraA--B--C--D--mzunguko;asy maandishiORChora mstari kupitia D sambamba na overlineBC, ukivuka overlineAB kwa E. Kisha BCDE ni sanjari, hivyo DE 12, EB 39, na AE 52 - 39 13. Hivyo DE2 AD2 AE2, na pembetatu ADE ni pembetatu ya kulia. Acha h iwe urefu kutoka D hadi overlineAE, na kumbuka kuwa textEneoADE frac12512 frac1213h,hivyo h 6013. Hivyo textAreaABCD frac6013cdotfrac1239 52 210.asyjozi A,B,C,D;A0,0;B4,0;C3.3,1;D0.3,1;leboA,A,S;leboB,B,S;leboC,C,N;leboD,D,N;kuchoraD--1,0;leboE,1,0,S;kuchoraA--B--C--D--mzunguko;asy 