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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 1. The second vertex is at the top of row 10 and the right of column 4. The third vertex is at the top of row 10 and the right of column 7.

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

(1 point)
Responses

12 square units
12 square units

24 square units
24 square units

14 square units
14 square units

28 square units
28 square units
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1 answer

To find the area of the triangle enclosed within the grid based on the provided vertices, we first need to identify the coordinates of the vertices.

  1. Vertex A: Row 2, Column 1 = (1, 2)
  2. Vertex B: Row 10, Column 4 = (4, 10)
  3. Vertex C: Row 10, Column 7 = (7, 10)

Now we can find the area of the triangle using the formula:

\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]

From the vertices:

  • The base can be considered as the segment between points B and C, which is on the same horizontal line (both at row 10).
  • The base length BC = column 7 - column 4 = 3 units.

To find the height, we calculate the vertical distance from vertex A to the line formed by base BC. Since B and C are both in row 10 (y=10) and vertex A is at row 2 (y=2):

  • Height = 10 - 2 = 8 units.

Now we can plug in the base and height into the area formula:

\[ \text{Area} = \frac{1}{2} \times 3 \times 8 = \frac{1}{2} \times 24 = 12 \text{ square units} \]

Thus, the area of the triangle is 12 square units. The correct response is:

12 square units.