1.
[tex]a = 20cm\\\\a) O = 4a = 4*20 = 80cm\\\\b) P = a^{2} = 20^{2} = 400 cm^{2}\\\\c) d = a\sqrt{2} = 20\sqrt{2} cm[/tex]
2.
[tex]a = 9 cm\\d = 15 cm\\\\a) a^{2} + b^{2} = d^{2}\\9^{2} + b^{2} = 15^{2}\\81 + b^{2} = 225\\b^{2} = 144\\b = 12 cm\\\\b) O = 2a + 2b = 2*9 + 2*12 = 18 + 24 = 42 cm\\\\c) P = a*b = 9*12 = 108 cm^{2}[/tex]
3.
[tex]a = 30 cm\\\\a) h = \frac{a\sqrt{3} }{2} = \frac{30\sqrt{3} }{2} = 15\sqrt{3} cm\\\\b) O = 3a = 3*30 = 90cm\\\\c) P = \frac{a^{2}\sqrt{3} }{4} = \frac{30^{2}\sqrt{3} }{4} = \frac{900\sqrt{3} }{4} = 225\sqrt{3} cm2[/tex]
4.
[tex]d_{1} = 6cm\\d_{2} = 8cm\\\\a) P = \frac{1}{2} * d_{1} * d_{2} = \frac{1}{2} * 6 * 8 = 24cm^{2}\\\\b) (\frac{1}{2} d_{1})^{2} + (\frac{1}{2}d_{2})^{2} = a^{2}\\\frac{1}{4} 6^{2} + \frac{1}{4}8{2}^{2} = a^{2}\\\frac{1}{4} 36 + \frac{1}{4}64 = a^{2}\\9 + 16 = a^{2}\\a^{2} = 25\\a = 5 cm\\c) O = 4a = 4*5 = 20cm[/tex]
5.
[tex]a = 8cm\\b = 20cm\\s = 10 cm\\\\a) O = a+b+s+s = 8+20+10+10 = 48cm\\\\b) x = (20-8)/2 = 12/2 = 6 cm\\h^{2} + x^{2} = s^{2}\\h^{2} + 6^{2} = 10^{2}\\h^{2} + 36 = 100\\^{2} = 64\\h = 8 cm\\\\c) P = \frac{1}{2} (a+b)h = \frac{1}{2}(8+20)*8 = \frac{1}{2}*28*8 = 112 cm^{2}[/tex]
