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Answer:

[tex]h\:=\:\:\frac{-\pi \:kr\:+\:S}{\pi \:r}[/tex]

Step-by-step explanation:

Given the expression

[tex]S=\pi \:r\left(h+k\right)\:[/tex]

  • Let us solve for h

[tex]S=\pi \:r\left(h+k\right)\:[/tex]

Flip the equation

[tex]\pi r\left(h+k\right)\:=\:S[/tex]

Apply distributive law:  [tex]a\left(b+c\right)=ab+ac[/tex]

[tex]\pi hr+\pi kr=S[/tex]      

Add -πkr to both sides

[tex]\pi hr+\pi kr+\left(-\pi kr\right)=S+\left(-\pi kr\right)[/tex]

[tex]\pi hr\:=\:-\pi kr\:+\:S[/tex]

Divide both sides by πr

[tex]\pi hr\:/\:\pi r\:=\:\:\frac{-\pi \:kr\:+\:S}{\pi \:r}[/tex]

[tex]h\:=\:\:\frac{-\pi \:kr\:+\:S}{\pi \:r}[/tex]

Therefore, we conclude that:

[tex]h\:=\:\:\frac{-\pi \:kr\:+\:S}{\pi \:r}[/tex]

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