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)

Answer 1

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.