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 2 and the right of column 4. The second vertex is at the top of row 9 and the right of column 4. The third vertex is at the top of row 6 and the right of column 9.

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

(1 point)
Responses

35 square units
35 square units

65 square units
65 square units

32.5 square units
32.5 square units

17.5 square units

Answer 1

To find the area of the non-right triangle based on the vertices given, they are located at the following coordinates:

1. First vertex (A): (4, 2)
2. Second vertex (B): (4, 9)
3. Third vertex (C): (9, 6)

Next, we can determine the lengths of the sides that will act as the base and height of the triangle.

1. **Base of the Triangle (from A to B):**
The distance from vertex A to vertex B is the vertical distance between their y-coordinates since both vertices have the same x-coordinate (4).
- Base (AB) = 9 - 2 = 7 units

2. **Height of the Triangle (from C perpendicular to line AB):**
The height corresponds to the horizontal distance from C (which has an x-coordinate of 9) to the line AB (which is a vertical line at x = 4).
- Height = 9 - 4 = 5 units

3. **Calculating the Area:**
The area \( A \) of a triangle can be computed using the formula:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
Plugging in the values:
\[
A = \frac{1}{2} \times 7 \times 5 = \frac{1}{2} \times 35 = 17.5 \text{ square units}
\]

Therefore, the area of the non-right triangle is **17.5 square units**.