The figure, as shown below, is made up of 6 identical triangles. If the area of the figure is 126 cm2 and its perimeter is 36 cm, find the height of each triangle (Figure not drawn to scale)
Let's assume the height of each triangle is $h$. Since there are 6 identical triangles, the total height of the figure is $6h$.
The base of each triangle is the same length as the perimeter of the figure, which is 36 cm. Since there are 3 triangles in the middle of the figure, the combined base of these triangles is $3 \times 36 = 108$ cm.
The area of each triangle is $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 36 \times h$. Since there are 6 triangles, the total area of the figure is $6 \times \frac{1}{2} \times 36 \times h = 126$ cm$^2$.
Therefore, we have $216h = 126$, so $h = \frac{126}{216} = \boxed{\frac{7}{12}}$ cm.