Odpowiedź:
1. Pp = 40*40 = 1600
[tex]40^{2} + x^{2} = 50^{2}[/tex] = 1600 + [tex]x^{2}[/tex] = 2500
2500 - 1600 = 900
[tex]x^{2}[/tex] = 900
x = [tex]\sqrt{900}[/tex] = 30
P = [tex]\frac{40*30}{2}[/tex] = 20*30 = 600
Pc = 1600 + 600*4 = 4000[tex]cm^{2}[/tex]
2. (rysunek taki sam jak w wcześniejszym zadaniu)
Pp = [tex]\sqrt{8} ^{2}[/tex] = 8
[tex]\sqrt{8} ^{2} + x^{2} = 5^{2}[/tex] = 8 + [tex]x^{2}[/tex] = 25
25 - 8 = 17
x = [tex]\sqrt{17}[/tex]
P = [tex]\frac{\sqrt{8}* \sqrt{17} }{2} = \frac{\sqrt{136} }{2} = \sqrt{16} = 4[/tex]
Pc = 8 + 4*4 = 24
3. Pp = [tex]\frac{3^{2\sqrt{3} } }{4}[/tex] = [tex]\frac{9\sqrt{3} }{4}[/tex]
Pb = [tex]\frac{3*6}{2}[/tex] = 9
Pc = 9*3 + [tex]\frac{9\sqrt{3} }{4}[/tex] = 27 + [tex]\frac{9\sqrt{3} }{4}[/tex]
4. Pp = 6 * [tex]\frac{8^{2\sqrt{3} } }{4}[/tex] = 16[tex]\sqrt{3}[/tex]
[tex]8^{2} + x^{2} = 14^{2}[/tex] = 64 + [tex]x^{2}[/tex] = 196
196 - 64 = 132
x = [tex]\sqrt{132}[/tex]
Pb = [tex]\frac{8*\sqrt{132} }{2} = 4\sqrt{132}[/tex]
Pc = 6 * 4[tex]\sqrt{132}[/tex] + 16[tex]\sqrt{3}[/tex] = 24[tex]\sqrt{132} + 16\sqrt{3}[/tex]
