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Question Number 180897 by depressiveshrek last updated on 18/Nov/22

Commented by depressiveshrek last updated on 18/Nov/22

$$\mid AB\mid =3$$$$\mid BC\mid =5$$$$BE=EC$$$$\mid CD\mid =1$$$$Findtheareaofthewhite\left(notthegrayone\right)area$$

Commented by manxsol last updated on 19/Nov/22

Commented by mr W last updated on 19/Nov/22

$$fine!$$$$butpleasepostansweras‘‘{answer}^{″},$$$$notas‘‘{comment}^{″}!$$

Commented by manxsol last updated on 19/Nov/22

$$itisunderstoodSr.W,excuseme$$

Commented by mr W last updated on 19/Nov/22

$$thanksalot!$$

Answered by mr W last updated on 19/Nov/22

Commented by mr W last updated on 19/Nov/22

$$AC=\sqrt{5^2-3^2}=4$$$$AE=BE=\frac{5}{2}$$$$DG=\frac{1}{4}\times AE=\frac{5}{8}$$$$CG=\frac{1}{4}\times CE=\frac{1}{4}\times \frac{5}{2}=\frac{5}{8}$$$$\frac{DF}{DB}=\frac{GE}{GB}=\frac{\frac{5}{2}-\frac{5}{8}}{5-\frac{5}{8}}=\frac{3}{7}$$$$\left[\mathrm{\Delta }AEB\right]=\frac{\left[\mathrm{\Delta }ABC\right]}{2}=\frac{3\times 4}{2\times 2}=3$$$$\left[\mathrm{\Delta }ADB\right]=\frac{3\times 3}{2}=\frac{9}{2}$$$$\left[\mathrm{\Delta }ADF\right]=\frac{3}{7}\times \left[ADB\right]=\frac{27}{14}$$$$whitearea=\frac{27}{14}+3=\frac{69}{14}$$

Commented by mr W last updated on 19/Nov/22

$$alternative:$$$$A(0,0)$$$$E(\frac{3}{2},2)$$$$D(0,3)$$$$eqn.ofAE:$$$$y=\frac{4x}{3}$$$$eqn.ofBD:$$$$y=3-x$$$$intersectionpointF:$$$$y=\frac{4x}{3}=3-x$$$$\Rightarrow x=\frac{9}{7},y=\frac{12}{7}$$$$\left[\mathrm{\Delta }AEB\right]=\frac{2\times 3}{2}=3$$$$\left[\mathrm{\Delta }ADF\right]=\frac{3}{2}\times \frac{9}{7}=\frac{27}{14}$$$$whitearea=3+\frac{27}{14}=\frac{69}{14}✓$$

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