We are asked to find the area of the triangle. The base of the triangle is $2\frac{2}{3} + \frac{8}{9}$ meters, and the height is $2\frac{1}{4}$ meters.

1. Problem Description

We are asked to find the area of the triangle. The base of the triangle is $2\frac{2}{3} + \frac{8}{9}$ meters, and the height is $2\frac{1}{4}$ meters.

2. Solution Steps

First, we need to find the length of the base by adding the two fractions.

$2\frac{2}{3} + \frac{8}{9} = 2 + \frac{2}{3} + \frac{8}{9} = 2 + \frac{6}{9} + \frac{8}{9} = 2 + \frac{14}{9} = 2 + 1\frac{5}{9} = 3\frac{5}{9}$

So the base is $3\frac{5}{9}$ meters.

Next, convert the base to an improper fraction.

$3\frac{5}{9} = \frac{3 \times 9 + 5}{9} = \frac{27+5}{9} = \frac{32}{9}$

Now convert the height to an improper fraction.

$2\frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8+1}{4} = \frac{9}{4}$

The formula for the area of a triangle is:

$Area = \frac{1}{2} \times base \times height$

Plug in the values for the base and height:

$Area = \frac{1}{2} \times \frac{32}{9} \times \frac{9}{4}$

Simplify:

$Area = \frac{1}{2} \times \frac{32}{1} \times \frac{1}{4} = \frac{1}{2} \times \frac{8}{1} \times \frac{1}{1} = \frac{8}{2} = 4$

3. Final Answer

The area of the triangle is 4 square meters.