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Question Number 95830 by I want to learn more last updated on 27/May/20

Answered by behi83417@gmail.com last updated on 28/May/20

4s+((16^2 )/2)=16^2 ⇒s=((16^2 )/8)=32

$$\mathrm{4s}+\frac{\mathrm{16}^{\mathrm{2}} }{\mathrm{2}}=\mathrm{16}^{\mathrm{2}} \Rightarrow\mathrm{s}=\frac{\mathrm{16}^{\mathrm{2}} }{\mathrm{8}}=\mathrm{32} \\ $$

Answered by john santu last updated on 28/May/20

Commented by john santu last updated on 28/May/20

shaded area = 8^2 −area OFDE  let OF = a ⇒ OD^2 =OF^2 +DF^2   64 = 2a^2  ⇒ a^2  = 32   then shaded area = 64−32 = 32

$$\mathrm{shaded}\:\mathrm{area}\:=\:\mathrm{8}^{\mathrm{2}} −\mathrm{area}\:\mathrm{OFDE} \\ $$$$\mathrm{let}\:\mathrm{OF}\:=\:\mathrm{a}\:\Rightarrow\:\mathrm{OD}^{\mathrm{2}} =\mathrm{OF}^{\mathrm{2}} +\mathrm{DF}^{\mathrm{2}} \\ $$$$\mathrm{64}\:=\:\mathrm{2a}^{\mathrm{2}} \:\Rightarrow\:\mathrm{a}^{\mathrm{2}} \:=\:\mathrm{32}\: \\ $$$$\mathrm{then}\:\mathrm{shaded}\:\mathrm{area}\:=\:\mathrm{64}−\mathrm{32}\:=\:\mathrm{32}\: \\ $$

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