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Question Number 197920 by cortano12 last updated on 04/Oct/23

Commented by cortano12 last updated on 04/Oct/23

$$\mathrm{if}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{shaded}\mathrm{is}320{\mathrm{cm}}^2$$$$\mathrm{then}\mathrm{find}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{big}\mathrm{triangle}.$$

Answered by Tokugami last updated on 04/Oct/23

$$\mathrm{shaded}\mathrm{area}\mathrm{is}320{\mathrm{cm}}^2$$$$\mathrm{first}n\mathrm{triangles}\mathrm{area}:A{\left(\frac{n}{10}\right)}^2=\frac{A}{100}{n}^2$$$$\mathrm{nth}\mathrm{wedge}\mathrm{area}=\frac{A}{100}(n^2-{(n-1)}^2)=\frac{A}{100}(2n-1)$$$$\frac{A}{100}[(2\left(9\right)-1)+(2\left(7\right)-1)+(2\left(5\right)-1)+(2\left(3\right)-1)+(2\left(1\right)-1)]=320$$$$\frac{A}{100}(17+13+9+5+1)=320$$$$\frac{45A}{100}=320$$$$A=\frac{6400}{9}{\mathrm{cm}}^2=711.11{\mathrm{cm}}^2$$$$$$

Answered by Sutrisno last updated on 14/Oct/23

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