To find the area of the triangle, we can use the formula for the area of a triangle given by:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Based on the description of the triangle within the 10 by 10 grid, we need to identify the vertices and calculate the base and height.
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Vertices:
- First vertex at (3, 1) (top of row 1, to the right of column 3)
- Second vertex at (1, 7) (top of row 7, to the left of column 1)
- Third vertex at (9, 1) (top of row 1, to the right of column 9)
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Base:
- The base can be taken as the horizontal distance between vertices (3, 1) and (9, 1).
- The distance = \(9 - 3 = 6\).
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Height:
- The height can be considered as the vertical distance from the base (row 1) to the y-coordinate of the vertex (1, 7), which has the y-coordinate 7.
- So, the height = \(7 - 1 = 6\).
Now we can substitute the base and height into the area formula:
\[ \text{Area} = \frac{1}{2} \times 6 \times 6 = \frac{1}{2} \times 36 = 18 \text{ square units} \]
Thus, the area of the non-right triangle is 18 square units.