$\text{a)}P=\frac{c+d}{2}\cdot h\mid \cdot \frac{2}{c+d}$  

$\underline{h=\frac{2P}{c+d}}$  

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$P=\frac{c+d}{2}\cdot h\mid \cdot \frac{2}{h}$  

$c+d=\frac{2P}{h}$  

$\underline{c=\frac{2P}{h}-d}$  

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$\text{b)}P=2\pi r\left(r+h\right)\mid :2\pi r$  

$r+h=\frac{P}{2\pi r}$  

$\underline{h=\frac{P}{2\pi r}-r}$  

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$\text{c)}P=2\left(ab+bc+ca\right)\mid :2$  

$ab+bc+ca=\frac{1}{2}P$  

$ab+ca=\frac{1}{2}P-bc$  

$a\left(b+c\right)=\frac{1}{2}P-bc\mid :\left(b+c\right)$  

$\underline{a=\frac{\frac{1}{2}P-bc}{b+c}}$  

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$\text{d)}P=\frac{a+b+c}{2}\cdot \frac{a+b-c}{2}$  

$P=\frac{\left(a+b\right)+c}{2}\cdot \frac{\left(a+b\right)-c}{2}$  

$P=\frac{{\left(a+b\right)}^2-c^2}{4}\mid \cdot 4$  

$4P={\left(a+b\right)}^2-c^2$  

$c^2={\left(a+b\right)}^2-4P$  

$\underline{c=\sqrt{{\left(a+b\right)}^2-4P}}$  

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$P=\frac{a+b+c}{2}\cdot \frac{a+b-c}{2}$  

$P=\frac{\left(a+b\right)+c}{2}\cdot \frac{\left(a+b\right)-c}{2}$  

$P=\frac{{\left(a+b\right)}^2-c^2}{4}\mid \cdot 4$  

$4P={\left(a+b\right)}^2-c^2$  

${\left(a+b\right)}^2=4P+c^2$  

$a+b=\sqrt{4P+c^2}$  

$\underline{a=\sqrt{4P+c^2}-b}$