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]
[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]
