27 cm
Explanation
let x represents the missing side.
the area of a triangle is given by:
[tex]\text{Area}=\frac{base\cdot heigth}{2}[/tex]
then
Let
base=27 cm
Area=364.5 square cm
heigth=x
replace,
[tex]\begin{gathered} \text{Area}=\frac{base\cdot heigth}{2} \\ \text{346.5}=\frac{27x}{2} \\ \text{Multiply both sides by 2} \\ \text{346.5}\cdot2=\frac{27x}{2}\cdot2 \\ 729=27x \\ \text{divide both sides by 27} \\ \frac{729}{27}=\frac{27x}{27} \\ 27=x \end{gathered}[/tex]
Hence, the heifht is 27 cm
