a) [latex]a-bok\ h-wysokosc\ \ z tw. Pitagorasa:\ \ h^2=a^2- (frac{1}{2}a)^2\ h^2=a^2- frac{1}{4} a^2\ h= sqrt{a^2- frac{1}{4}a^2 }\ h= sqrt{ frac{3}{4}a^2} \ h= frac{1}{2} a sqrt{3} \ h= frac{a sqrt{3} }{2} \ P= frac{1}{2} ah\ P= frac{1}{2} a* frac{a sqrt{3} }{2} \ P= frac{a^2 sqrt{3} }{4} [/latex] b) O=30√3 O=3a 30√3=3a a=10√3 [latex]P= frac{a^2 sqrt{3} }{4} \ P= frac{(10 sqrt{3})^2 sqrt{3} }{4} \ P= frac{300 sqrt{3} }{4} \ P=75 sqrt{3} \[/latex] c) h=4 cm [latex]h= frac{a sqrt{3} }{2} \ 4= frac{a sqrt{3} }{2} \ 8=a sqrt{3} \ a= frac{8}{ sqrt{3} }\ a= frac{8 sqrt{3} }{3} cm\ P= frac{a^2 sqrt{3} }{4} \ P= frac{( frac{8 sqrt{3} }{3})^2 sqrt{3} }{4} \ P= frac{ frac{192 sqrt{3} }{9} }{4} \ P= frac{192 sqrt{3} }{36}\ P=5 frac{1}{3} sqrt{3} cm^2 [/latex]
[latex]a)\P= frac{a*h}{2} o pole trojkata\ \h^2=a^2-( frac{a}{2})^2\ \h^2= frac{4a^2-a^2}{4}= frac{3a^2}{4}\ \h= frac{asqrt3}{2}\ \P= frac{a}{2}* frac{asqrt3}{2}= frac{a^2sqrt3}{4} [/latex] b) [latex]Obw=3a=30sqrt3\ \a=10sqrt3\ \P= frac{(10sqrt3)^2sqrt3}{4}= 75sqrt3[j^2] [/latex] c) [latex] frac{a}{2}*sqrt3=4\ \a= frac{8}{sqrt3}\ \P= frac{(frac{8}{sqrt3})^2*sqrt3}{4}= frac{64sqrt3}{3*4}= frac{16sqrt3}{3}[j^2] [/latex]
