图 ABCD 显示了两个直角三角形 ABC 和 ACD 在线段 AC 处拼接在一起。求阴影区域 AECF 的面积。 答：___ cm$^2$

1. Identify the shaded area as the sum of two triangles

The shaded area AECF is composed of two triangles: $\triangle ACF$ and $\triangle ACE$.

2. Calculate the area of triangle ACF

In $\triangle ABC$, the height corresponding to the base $CF$ is $AB = 9\text{ cm}$.
Area of $\triangle ACF = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 16 \times 9 = 72\text{ cm}^2$.

3. Calculate the area of triangle ACE

In $\triangle ACD$, the height corresponding to the base $AE$ is $CD = 14\text{ cm}$.
Area of $\triangle ACE = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 10 \times 14 = 70\text{ cm}^2$.

4. Calculate the total shaded area

Total shaded area = Area of $\triangle ACF$ + Area of $\triangle ACE$ = $72 + 70 = 142\text{ cm}^2$.