Calculate Triangle Area with 2/3 Segment Ratio and Height of 9 Units

To solve this problem, we'll follow these steps:

• Step 1: Calculate the length of side BC using the given ratio.
• Step 2: Find the area of the triangle using the area formula.
• Step 3: Verify the solution with the provided choice options.

Now, let's work through each step:

Step 1: Side AE is provided as 9. Since side BC is $\frac{2}{3}$ of side AE, we calculate:

$BC = \frac{2}{3} \times AE = \frac{2}{3} \times 9 = 6$

Step 2: Because triangle ABC is involved in calculation, the area of triangle BCE becomes $\text{Area} = \frac{1}{2} \times BC \times height$, and assumed height perfectly completes these side lengths within the triangle grid. Given no specific height, the functional area equals set simplification calculations:

Substitute the values to find the area of triangle BCE:

$\text{Area of } \triangle BCE = \frac{1}{2} \times BC \times AE = \frac{1}{2} \times 6 \times 9$

Calculate:

$\text{Area} = \frac{1}{2} \times 54 = 27$

Therefore, the solution to the problem is $27$.