To find the area of the triangle in the image, we can apply the following method based on the grid:

Steps:

1. Count the base and height:

   • Each square in the grid is 1 unit by 1 unit.
   • The base of the triangle is along the bottom row, and it spans 4 grid squares.
   • The height of the triangle (the vertical distance from the base to the opposite vertex) spans 4 grid squares.

2. Use the area formula for a triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ Substituting the base and height values (both 4 units): $\text{Area} = \frac{1}{2} \times 4 \times 4 = \frac{1}{2} \times 16 = 8 \text{ square units}.$

Thus, the area of the triangle is 8 square units.

Would you like more details or have any questions?

Here are some related questions to expand this concept:

1. How would the area change if the base was halved?
2. What is the perimeter of this triangle based on the grid?
3. How would the area change if the height were doubled?
4. How could we apply the Pythagorean theorem to find the hypotenuse of the triangle?
5. How does the triangle's area compare to that of a rectangle with the same base and height?

Tip: Always ensure that the base and height of a triangle are perpendicular to each other when applying the area formula.