Question

Use the image to answer the question.

An illustration shows a 10 by 10 grid. A non-right triangle is enclosed within the grid. The first vertex is at the top of row 1 and the right of column 3. The second vertex is at the top of row 7 and the left of column 1. The third vertex is at the top of row 1 and the right of column 9.

What is the area of the non-right triangle? The base and height are found by counting the squares.

(1 point)
Responses

27 square units
27 square units

18 square units
18 square units

54 square units
54 square units

45 square units
45 square units
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Answer 1

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.

1. **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)

2. **Base**:
- The base can be taken as the horizontal distance between vertices (3, 1) and (9, 1).
- The distance = \(9 - 3 = 6\).

3. **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**.