??? ??????? ??????????? ????? ???? ? ???? ????? ?? ????????? ??????? ? ??????? ?????? ???????????????? ?????????? ???????? ????????????? ? ??????????? ????? ????????? ????????? ?????? ????????? ?????? ?? ?????????

???????, ??????????, ??? ??????????? ? ?????? ??????????? ??? ?????????? ???????? ????? ???????? ?????? ? ??????????? ????? ???? ??????????? ????????? ????????????, ??? ????????? ? ???????? ????????? ?????????? ??????????? ??? ????? ?????????????, ?? ????????? ? ??? ??????????? ?? ?????? ???????? ??????

???????? ?????? ????????????? ??? ????????????? ?, ???? ?????????? ???????? ? ????? ???????? ???, ??????, ????? ??, ?? ??????? ???????? 16.3 ?? ² ?, ??? ?? ????????? ?, ?? ????? ??????? ?????????? ???????? ????? ????????? ? 16.3 ??? 1×1 ?? ???????? ????????????? ???????? ?????? ????????????? ????????? ??????? ?? ??????????????

???????????? ???? ??????????? ??????????????, ?????? ? ????, ????? ???????? ??????? ?????????

???????????? ?????????? ???????? ?????????? ????????? ?????? ????????? ? ???????????? ????????? ???????? ???????? ???????? ????????????? ?????? ?????????? ??????????? ???????????, ??? ???????? ? ???????????? ?????????? ????? ???? ???? ??????

???????????? ???????? ??????? ?????????? ????? ??????????? ?? ?????? ?????????? ????? ?????????

??????? ?????????????? ????????? [ ???????? | ???????? ???? ]

???????? ???????? ?, ??? ???? ??????? ???????????????.

• ??????, ??????? ???????? ???? ?????? ?;
• ????????, ??????? ??????? ???????? ??????? ? ???????????? ????? ??????? ?????? ??? ?????????? ??????????? ????????? ????? ????????? ?????? ??????;
• ??????????????, ??????? ???????? ?????????? ??????????? ???? ??????? ??;
• ???????????, ??????? ?????? ?????????? ???????? ??????? ? ?????

???? ????????? [ ???????? | ???????? ???? ]

??????????? ????????????? ???????? ??????????????? ? ???????? ??? ???????, ??? ????? ??????????? ??? ????????? ?????????? ???????? ??

?????????? ?????????? ??????????? ???????? ??????? ? ????????? ?????, ??? ??? ????????? ???????? ??????????? ???? ?? ??? ??????

1? ² =100?? ² =1000000?? ² =10 ^-6 ?? ² :

????????? ????? ??????? ????? ??? ???.?. ?.(???????), ?.?. ?.(???????), ? ² ?

??? ????????? [ ???????? | ???????? ???? ]

1??=100 ????????? ????

?????? ????, ?? ?? ? ????? ? ???? ???????????????, ?????? ? ???? ???????? ?????? ???????? ????????? ?????? ??

1??????(??)=100??=10 000 ????????? ????=0.01 ????????? ???????? (?? ² )

???? ?????? ????? ???????? ??????? ? ??? ??

1???=4 840 ????????? ????=43 560 ????????? ???????=4046.86 ????????? ?????

???? ??????? ? ??????? ??????????? 40%-??

???????????? ?????????? ??????????? ???????? [ ???????? | ???????? ???? ]

???????	???????	?????????????
????????? (????????????) ?????????	${\displaystyle {\frac {1}{4}}{\sqrt {3}}s^{2}\,\!}$	${\displaystyle s}$-? ??????????? ????? ????????????? ??
??????????	${\displaystyle {\sqrt {s(s-a)(s-b)(s-c)}}\,\!}$	${\displaystyle s}$-? ???????????? ?, ${\displaystyle a}$-?, ${\displaystyle b}$-? ? ${\displaystyle c}$-? ??????? ???????????????? ???
	${\displaystyle {\tfrac {1}{2}}ab\sin(C)\,\!}$	${\displaystyle a}$-? ? ${\displaystyle b}$-? ????? ???? ??????? ??, ${\displaystyle C}$-?? ????? ?????? ???????? ?
	${\displaystyle {\tfrac {1}{2}}bh\,\!}$	${\displaystyle b}$-? ? ${\displaystyle h}$-? ??????????? ????? ?? ????????????? ???
???????????	${\displaystyle {\tfrac {1}{2}}ab}$	${\displaystyle a}$-? ? ${\displaystyle b}$-? ????????????? ???
????????????	${\displaystyle bh\,\!}$	${\displaystyle b}$-? ????? ????????????? ?, ${\displaystyle h}$-?? ??????????????
?????	${\displaystyle {\tfrac {1}{2}}(a+b)h\,\!}$	${\displaystyle a}$-? ? ${\displaystyle b}$-? ???????? ??????? ?? (???????) ${\displaystyle h}$-?? ????? ???? ???? ????????????????
?????	${\displaystyle \pi r^{2}\ {\text{???}}\ {\frac {\pi d^{2}}{4}}\,\!}$	${\displaystyle r}$-? ???????? ?, ${\displaystyle d}$-?? ??????????
?????? ??????	${\displaystyle {\frac {\theta }{2}}r^{2}\ {\text{???}}\ {\frac {L\cdot r}{2}}\,\!}$	${\displaystyle r}$-? ${\displaystyle \theta }$-? ???????? ?? ???????? ??????????? , ${\displaystyle L}$-? ???????? ??
?????	${\displaystyle \pi ab\,\!}$	${\displaystyle a}$-? ? ${\displaystyle b}$-? ?????????????? ???

??????????? ???????? [ ???????? | ???????? ???? ]

????? [ ???????? | ???????? ???? ]

${\displaystyle \mathrm {S} =\pi r^{2}.\,}$ ${\displaystyle \mathrm {S} ={\frac {\pi d^{2}}{4}}\,}$ ????? r-? ?????? ???????? ? ??? d-? ?????????

????????? [ ???????? | ???????? ???? ]

${\displaystyle \mathrm {S} =a^{2}.\,}$

????????? [ ???????? | ???????? ???? ]

1. ${\displaystyle \mathrm {S} ={\frac {1}{2}}bh}$# ${\displaystyle S_{\triangle ABC}={\frac {1}{2}}bh_{b}}$, ???? ?? ${\displaystyle \ h_{b}=a\sin \gamma }$, ?????
2. ${\displaystyle S_{\triangle ABC}={\frac {1}{2}}ab\sin \gamma }$
3. ${\displaystyle S_{\triangle ABC}={\frac {1}{2}}r(a+b+c)=pr}$
4. ${\displaystyle S_{\triangle ABC}={\frac {abc}{4R}}}$
5. ${\displaystyle S_{\triangle ABC}={\sqrt {p(p-a)(p-b)(p-c)}}={1 \over 4}{\sqrt {(a+b+c)(b+c-a)(a+c-b)(a+b-c)}}}$ - ?????? ??????
6. ${\displaystyle S_{\triangle ABC}={\frac {a^{2}\sin \beta \sin \gamma }{2\sin \alpha }}}$
7. ${\displaystyle S_{\triangle ABC}={2R^{2}\sin \alpha \sin \beta \sin \gamma }}$
8. ${\displaystyle S_{\triangle ABC}={\frac {1}{2}}{\begin{vmatrix}x_{A}&y_{A}&1\\x_{B}&y_{B}&1\\x_{C}&y_{C}&1\end{vmatrix}}={\frac {\left|x_{A}(y_{B}-y_{C})+x_{B}(y_{C}-y_{A})+x_{C}(y_{A}-y_{B})\right|}{2}}=}$
   ${\displaystyle ={\frac {\left|(x_{B}-x_{A})(y_{C}-y_{A})-(x_{C}-x_{A})(y_{B}-y_{A})\right|}{2}}}$
9. ${\displaystyle S_{\triangle ABC}={\frac {ab}{2}}=r^{2}+2rR}$ - ??????????? ???????? ?????
10. ${\displaystyle S_{\triangle ABC}={\frac {c^{2}}{2(ctg\alpha +ctg\beta )}}}$ - ??? ?????? ? ???????? ??? ????? ? ???? ??? ???????????

?????

• ${\displaystyle \ h_{b}}$ - ${\displaystyle \ b}$ ??????? ?????? ????????????? ?,
• ${\displaystyle p={\frac {a+b+c}{2}}}$ - ??????? ???? ?,
• ${\displaystyle \ r}$ - ??????? ?????? ???????? ?,
• ${\displaystyle \ R}$ - ???????? ?????? ???????? ?,
• ${\displaystyle \ (x_{A},y_{A});(x_{B},y_{B});(x_{C},y_{C})}$ - ???????? ????????? ????????????? ???

????? [ ???????? | ???????? ???? ]

${\displaystyle a}$ ? ${\displaystyle b}$ ?????? ??????? ${\displaystyle m}$ ????? ??? ? ${\displaystyle h}$ ? ??????????? ????????

${\displaystyle S={\frac {(a+b)}{2}}h=\displaystyle mh}$

?????? ???????? ${\displaystyle a}$, ${\displaystyle b}$ ??????? ? ${\displaystyle c}$ ? ${\displaystyle d}$ ?? ???????? ??????? ????????

${\displaystyle S={\frac {a+b}{4|a-b|}}{\sqrt {(a+c+d-b)(a+d-b-c)(a+c-b-d)(b+c+d-a)}}.}$

???????????? ?????? ???????? ${\displaystyle r}$ ???????? ????????? ???????? ? ?????? ??? ${\displaystyle \alpha }$ ?????? ????????

${\displaystyle S={\frac {4r^{2}}{\sin {\alpha }}}}$

????????????, ??? ????? ???????? 30° ?, ???

${\displaystyle S=\displaystyle 8r^{2}}$