Question

помогите срочно молю геометрия

Answer 1

$P=na \ a=2Rsin frac{180}{n} \ r=Rcos frac{180}{n}$

1)
$a=2Rsin frac{180}{n} =2cdot3 sqrt{2} sin frac{180}{4} =6 sqrt{2} cdot frac{ sqrt{2} }{2} =6(sm) \ P=na=4cdot6=24(sm) \ r=Rcos frac{180}{n} =3 sqrt{2} cos frac{180}{4} =3 sqrt{2} cdot frac{ sqrt{2} }{2} =3(sm)$

2)
$a= frac{P}{n} = frac{24}{3} =8(sm) \ R= cfrac{a}{2sin frac{180}{n} } = cfrac{8}{2sin frac{180}{3} } = cfrac{4}{ frac{ sqrt{3} }{2} } = frac{8 sqrt{3} }{3}(sm) \ r=Rcos frac{180}{n} =frac{8 sqrt{3} }{3} cdot cos frac{180}{3} =frac{8 sqrt{3} }{3} cdot frac{1}{2} =frac{4 sqrt{3} }{3}(sm)$

3)
$R= cfrac{r}{cos frac{180}{n} } =cfrac{9}{cos frac{180}{6} } =cfrac{9}{frac{ sqrt{3} }{2} } = 6sqrt{3}(sm) \ a=2Rsin frac{180}{n} =2cdot6 sqrt{3}sin frac{180}{6} =12sqrt{3}cdot frac{1}{2} =6sqrt{3}(sm) \ P=na=6cdot6 sqrt{3} =36 sqrt{3}(sm)$

4)
$R= cfrac{r}{cos frac{180}{n} } =cfrac{5 sqrt{3} }{cos frac{180}{3} } =cfrac{5 sqrt{3} }{frac{ 1 }{2} } =10 sqrt{3} (sm) \ a=2Rsin frac{180}{n} =2cdot10 sqrt{3} sin frac{180}{3} =20sqrt{3}cdot frac{ sqrt{3} }{2} =30(sm) \ P=na=3cdot30 =90(sm)$