<prompt> Katika mchoro, R iko kwenye QS na QR8. Pia, PR12, angle PRQ120circ, na angle RPS 90circ. Eneo la pembetatu QPS ni nini? asyC19ukubwa cm 10; REKEBISHAkuagiza olympiad; Viratibu vya pointijozi r 0, 0;jozi q -8, 0;jozi p 12 dir 60;jozi s 24, 0; chora mistarichorap--s--r--p--q--r; leboleboR, r, S;leboQ, q, SW;leboS, s, SE;leboP, p, N;lebo12, r p - r 2, SE;lebo8, r q - r 2, S;lebo120circ, r, NW 0.2 E;markscalefactor 0.08;chorarightanglemarkr, p, s;asy  <response>: Kwa kuwa angle QRP120circ na QRS ni mstari wa moja kwa moja, basi angle PRS 180circ - 120circ 60circ.Kwa kuwa angle RPS 90circ, basi pembetatu SRP ni 30circ-60circ-90circ pembetatu.Kwa hiyo, RS 2PR21224.Dondosha herufi moja kwa moja kutoka P hadi T kwa RS. asyC20Sukubwa cm 10; REKEBISHAkuagiza olympiad; Viratibu vya pointijozi r 0, 0;jozi q -8, 0;jozi p 12 dir 60;jozi s 24, 0;jozi t p.x, 0; chora mistarichorap--s--r--p--q--r;chorap--t; leboleboR, r, S;leboQ, q, SW;leboS, s, SE;leboP, p, N;leboT, t, S;lebo12, r p - r 2, SE 0.2 W;lebo8, r q - r 2, S;lebo120circ, r, NW 0.2 E;lebo60circ, r, 2 NE E;markscalefactor 0.08;chorarightanglemarkr, p, s;choraalama ya kuliap, t, s;asy Kwa kuwa angle PRT60circ na angle PTR 90circ, basi pembetatu PRT pia ni 30circ-60circ-90 circ pembetatu.Kwa hivyo, PT fracsqrt32PR 6sqrt3.Zingatia pembetatu QPS. Tunaweza kuzingatia QS kama msingi wake wenye urefu wa PT.Kwa hivyo, eneo lake ni frac126sqrt382496sqrt3. 