1. 70cm-175% x-100% x=70cm*100%/175% x=40cm Obojętnie jakie przyjmiemy boki podstawy, ważne by obwód się zgadzał, więc a=30, b=5, bo L=2*(a+b), L=2*(30+5)=2*35=70(cm) Pb=2*(40cm*30cm)+2*(40cm*5cm) Pb=2*1200cm²+2*200cm² Pb=2400cm²+400cm² Pb=2800cm² 2. a=2n H=2n+½*2n=2n+n=3n Pc=2Pp+Pb Pp=a² Pp=(2n)²=4n² Pb=4aH Pb=4*2n*3n=24n² Pc=2*4n²+24n²=8n²+24n²=32n² V=PpH V=4n²*3n=12n³ 3. d kwadratu=√288=12√2cm d=a√2=12√2 a=12cm=krawędź podstawy h=⅓a=⅓×12=4cm v=a²h=12²×4=576cm³ Pp=a²=12²=144cm² Pb=4ah=4×12×4=192 Pc=2×144+192=480cm² 4. H = 20 cm d1 = 10 cm d2 = ? P = 240 cm² Pole jednej podstawy: P = 240/2 = 120 cm² P = 1/2*d1*d2 << pole rombu 120 = 1/2*10*1/2*d2 5*1/2*d2 = 120 5/2*d2 = 120 |:5/2 d2 = 48 cm z tw. Pitagorasa a² = (1/2d1)²+(1/2d2)² a² = 5²+24² a² = 25+576 a² = 601 a = √601 cm Pc = 240+4*a*H Pc = 240+4*√601*20 Pc = 240+80√601 Pc = 80(3+√601) cm² V = Pp*H V = 120*20 V = 2400 cm³
