To find the area of the triangle formed by the vertices, we can use the formula for the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
From the coordinates provided for the vertices:
- Vertex A (top of row 2, right of column 4): A(4, 2)
- Vertex B (top of row 9, right of column 4): B(4, 9)
- Vertex C (top of row 6, right of column 9): C(9, 6)
Step 1: Find the base and height
Base: The distance between points A and B represents the height of the triangle when considering the base on the line through points A and C.
The base can be determined by the horizontal distance between points A and C:
- A is at (4, 2)
- C is at (9, 6)
Base Length Calculation: \[ \text{Base} = |x_C - x_A| = |9 - 4| = 5 \text{ units} \]
Height: The height can be determined as the vertical distance from point B to the line segment AC. The y-coordinates of A and B are respectively 2 and 9, meaning the height is the vertical distance from A to B, which measures how tall the triangle is.
Height Length Calculation: \[ \text{Height} = |y_B - y_A| = |9 - 2| = 7 \text{ units} \]
Step 2: Calculate the Area
Now that we have base and height, we can compute the area of the triangle:
\[ \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 5 \times 7 = \frac{35}{2} = 17.5 \text{ square units} \]
Thus, the area of the triangle is:
\[ \text{Area} = 17.5 \text{ square units} \]
Answer:
17.5 square units