Rysunek pomocniczy w zalacznikach
a)
a = 2cm
b = 7cm
h = 4cm
[tex]4^2+3^3=c^2\\16+9=c^2\\c = 5[/tex]
[tex]4^2+2^2=d^2\\16+4=d^2\\d = \sqrt{20} = 2\sqrt{5}[/tex]
[tex]P = \frac{(a+b)*h}{2} = \frac{(2+7)*4}{2} = 9*2=18cm^2\\Ob = a+b+c+d=2+7+4+2\sqrt{5}=13+2\sqrt{5}cm[/tex]
b)
[tex]7^2+1^2=a^2\\49+1=a^2\\a = \sqrt{50} = 5\sqrt{2}[/tex]
[tex]3^2+5^2=b^2\\9+25=b^2\\b = \sqrt{34}[/tex]
[tex]6^2+4^2=c^2\\36+16=c^2\\c = \sqrt{52}=2\sqrt{13}[/tex]
[tex]Ob = a+b+c\\Ob = 5\sqrt{2}+\sqrt{34}+2\sqrt{13}cm[/tex]
[tex]P=6*7-(\frac{6*4}{2}+\frac{7*1}{2}+\frac{3*5}{2})= 42-\frac{46}{2} =42-23=19cm^2[/tex]
c)
[tex]3^2+2^2=a^2\\9+4=a^2\\a = \sqrt{13}[/tex]
[tex]Ob=4\sqrt{13}[/tex]
[tex]P=5^2-2(\frac{(2+5)*2}{2} + \frac{2*3}{2})\\P = 25-2(7+3)=25-20=5cm^2[/tex]
