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

32 square units
32 square units

48 square units
48 square units

64 square units
64 square units

24 square units

Answer 1

To find the area of the non-right triangle described by the vertices at (6, 1), (1, 7), and (9, 7), we can follow these steps:

1. Identify the vertices:

   • Vertex A (6, 1)
   • Vertex B (1, 7)
   • Vertex C (9, 7)

2. Determine the base and height:

   • The base can be considered as the distance along the row at y = 7 from point B to point C (from (1, 7) to (9, 7)).

   • The length of the base = x-coordinate of C - x-coordinate of B = 9 - 1 = 8 units.

   • The height is the vertical distance from point A (6, 1) to the line y = 7, which is:

   • Height = y-coordinate of B (or C) - y-coordinate of A = 7 - 1 = 6 units.

3. Calculate the area: The area of a triangle is given by the formula: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] Plugging in our values: \[ \text{Area} = \frac{1}{2} \times 8 \times 6 = \frac{48}{2} = 24 \text{ square units} \]

Thus, the area of the non-right triangle is 24 square units.