Геометрична зад.

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IMG-282008844ac5a27c435056942b0c8fef-V.jpg (132.62 KiB) Прегледано 485 пъти

[ammornil]

[tex]ABCD \cong A_{1}B_{1}C_{1}D_{1}, \hspace{1.2em} AB\| CD, \hspace{1.2em} AD\bot CD, \hspace{1.2em} AD\bot AB[/tex]
[tex]AA_{1}\| BB_{1}\| CC_{1}\| DD_{1}, \hspace{1.2em} AA_{1}\bot p(ABCD), \hspace{1.2em} AA_{1}\bot p(A_{1}B_{1}C_{1}D_{1})[/tex]

[tex]AB=A_{1}B_{1}=a, \hspace{1.2em} CD=C_{1}D_{1}=b, \hspace{1.2em} AD=A_{1}D_{1}=c, \hspace{1.2em} BC=B_{1}C_{1}=d, \hspace{1.2em} AA_{1}=BB_{1}=CC_{1}=DD_{1}=H[/tex]
[tex]a=10[cm], \hspace{1.2em} b=7[cm], \hspace{1.2em} c=4[cm], \hspace{1.2em} d=5[cm], \hspace{1.2em} H=15[cm][/tex]

[tex]P=a+b+c+d=10+7+4+5=26[cm] \rightarrow S=P\cdot{H}=26\cdot{15}=390[cm^{2}][/tex]

[tex]AD\bot CD \Rightarrow B=\frac{a+b}{2}\cdot{c}=\frac{10+7}{2}\cdot{4}=17\cdot{2}=34[cm^{2}] \Rightarrow S_{1}=2\cdot{B}+S=2\cdot{34}+390=458[cm^{2}][/tex]

[tex]V=B\cdot{H}=34\cdot{15}=510[cm^{3}][/tex]

[tex][/tex]