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Question Number 63194 by lalitchand last updated on 30/Jun/19

Answered by mr W last updated on 30/Jun/19

$$\frac{\mathrm{\Delta }AQR}{\mathrm{\Delta }ABC}={\left(\frac{AQ}{AB}\right)}^2={\left(\frac{2}{3}\right)}^2=\frac{4}{9}$$$$\frac{\mathrm{\Delta }APS}{\mathrm{\Delta }ABC}={\left(\frac{AP}{AB}\right)}^2={\left(\frac{1}{3}\right)}^2=\frac{1}{9}$$$$\frac{◻PQRS}{\mathrm{\Delta }ABC}=\frac{\mathrm{\Delta }AQR-\mathrm{\Delta }APS}{\mathrm{\Delta }ABC}=\frac{\mathrm{\Delta }AQR}{\mathrm{\Delta }ABC}-\frac{\mathrm{\Delta }APS}{\mathrm{\Delta }ABC}=\frac{4}{9}-\frac{1}{9}=\frac{3}{9}=\frac{1}{3}$$

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