Simple Polygon Area

Solution:
Let us denote the given side with a and the side whose length we are trying to find with b. We have that [tex]S=a.b[/tex], therefore [tex]b=\frac{S}{a}=\frac{18cm^2}{6cm}=3cm[/tex].

Solution:
CD and AB are the parallel sides in a rectangle, so they have equal lengths. Therefore, CD=5.

Solution:
The area of a rectangle is calculated by the formula S=AB.BC, so [tex]BC=\frac{S}{AB}=\frac{35cm^2}{5cm}=7cm[/tex].

Solution:
Let us denote the catheti with a and b. We know that a=9cm. We also know that [tex]\frac{1}{2}a.b=S[/tex] => [tex]b=\frac{2S}{a}=\frac{2.36}{9}=8cm[/tex]

Solution:
We know that [tex]S_{ABC}=\frac{1}{2}AB.CH[/tex], therefore [tex]CH=\frac{2S_{ABC}}{AB}=\frac{2.28}{8}=7[/tex].

Solution:
We know that [tex]S=\frac{1}{2}.AH.BC[/tex], so [tex]AH=\frac{2S}{BC}=\frac{2.58cm^2}{4cm}=29cm[/tex]

Solution:
We know that [tex]S=\frac{1}{2}.AC.BH[/tex] => [tex]AC=\frac{2S}{BH}=\frac{2.44cm^2}{11cm}=8cm[/tex].