Category: Geometry

Question Number 5529 by Rasheed Soomro last updated on 18/May/16 Commented by Rasheed Soomro last updated on 18/May/16 $$\bigtriangleup\mathrm{ABC}\:\mathrm{is}\:\mathrm{an}\:\mathrm{equilaterl}\:\mathrm{triangle}. \\ $$$$\mathrm{D},\mathrm{E},\mathrm{F}\:\mathrm{are}\:\mathrm{mid}-\mathrm{points}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sides}. \\ $$$$\mathrm{The}\:\mathrm{centres}\:\mathrm{of}\:\mathrm{arcs}\:\mathrm{are}\:\mathrm{vertices}\:\mathrm{of} \\ $$$$\bigtriangleup\mathrm{ABC}.…

Question Number 5515 by FilupSmith last updated on 17/May/16 $$\mathrm{If}\:\mathrm{you}\:\mathrm{have}\:\mathrm{a}\:\mathrm{regular}\:{n}−\mathrm{sided}\:\mathrm{polygon}, \\ $$$$\mathrm{is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{method}\:\mathrm{to}\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{area} \\ $$$$\mathrm{from}\:\mathrm{one}\:\mathrm{corner}\:\mathrm{to}\:\mathrm{another}? \\ $$$$ \\ $$$$\mathrm{That}\:\mathrm{is},\:\mathrm{if}\:\mathrm{we}\:\mathrm{start}\:\mathrm{at}\:\mathrm{a}\:\mathrm{corner}\:\left(\mathrm{corner}\:\mathrm{1}\right), \\ $$$$\mathrm{and}\:\mathrm{draw}\:\mathrm{a}\:\mathrm{line}\:\mathrm{to}\:\mathrm{corner}\:{x},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{area}? \\ $$$$\mathrm{See}\:\mathrm{image}\:\mathrm{in}\:\mathrm{comment}\:\mathrm{for}\:\mathrm{visual}\:\mathrm{representation}. \\ $$ Commented…

Question Number 5490 by 123456 last updated on 16/May/16 $$\int\sqrt{{r}^{\mathrm{2}} −{x}^{\mathrm{2}} }{dx}=? \\ $$$$\underset{−{r}} {\overset{{x}} {\int}}\sqrt{{r}^{\mathrm{2}} −{x}^{\mathrm{2}} }{dx}=?? \\ $$$$\underset{{x}} {\overset{{y}} {\int}}\sqrt{{r}^{\mathrm{2}} −{x}^{\mathrm{2}} }{dx}=??? \\…

Question Number 5447 by 3 last updated on 15/May/16 $$\mathrm{6}/\mathrm{8} \\ $$$$ \\ $$ Answered by FilupSmith last updated on 15/May/16 $$\frac{\mathrm{6}}{\mathrm{8}}=\frac{\mathrm{2}×\mathrm{3}}{\mathrm{2}×\mathrm{4}} \\ $$$$=\frac{\mathrm{2}}{\mathrm{2}}×\frac{\mathrm{3}}{\mathrm{4}} \\…

Question Number 5417 by FilupSmith last updated on 14/May/16 $$\mathrm{Prove},\:\mathrm{or}\:\mathrm{disprove},\:\mathrm{that}\:\mathrm{the}\:\mathrm{circle} \\ $$$$\mathrm{has}\:\mathrm{the}\:\mathrm{largest}\:{Perimiter}\:\mathrm{over}\:\mathrm{all} \\ $$$$\mathrm{natural}\:\mathrm{shapes}\:\mathrm{that}\:\mathrm{have}\:\mathrm{area}\:{A} \\ $$ Commented by Rasheed Soomro last updated on 14/May/16 $$\mathrm{I}\:\mathrm{think}\:\mathrm{that}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{has}\:\mathrm{the}\:\mathrm{smallest}…