Three points of a 5x5 square array are connected. How many square units are in the area of the largest possible triangle that can be formed?

15

12.5

25

75 To find the largest possible triangle that can be formed with three points in a 5x5 square array, we need to consider all the possible triangles that can be formed by connecting any three points on the square.

Let's start by visualizing the square array:

```
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
```

Now, each point in the square has 4 possible neighboring points to which it can be connected. This means there are 4 choose 3 (written as 4C3) ways to choose three points on the square.

4C3 = 4! / (3! * (4-3)!) = 4! / (3! * 1!) = 4

So, there are 4 possible triangles that can be formed by connecting any three points on the square.

Next, we need to determine the area of each triangle. Since the square has side length of 5 units, each unit square within the array has an area of 1 square unit.

The largest possible triangle that can be formed will be an equilateral triangle with side length 5 units. To calculate its area, we can use the formula for the area of an equilateral triangle:

Area = (sqrt(3) / 4) * side length^2

Substituting the values, we get:

Area = (sqrt(3) / 4) * 5^2 = (sqrt(3) / 4) * 25 = (25 sqrt(3)) / 4

Hence, the area of the largest possible triangle that can be formed in the 5x5 square array is (25 sqrt(3)) / 4 square units.