Use the image to answer the question.

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

64 square units
64 square units

32 square units
32 square units

24 square units
24 square units

48 square units
48 square units
Skip to navigation

Answer 1

To find the area of the triangle described, we need to identify the coordinates of each vertex based on the grid layout provided.

1. Vertices of the triangle:

   • First vertex: (6, 1)
   • Second vertex: (1, 7)
   • Third vertex: (9, 7)

2. Visualizing the vertices:

   • The first vertex (6, 1) is in the first row, sixth column.
   • The second vertex (1, 7) is in the seventh row, first column.
   • The third vertex (9, 7) is in the seventh row, ninth column.

3. Finding the base and height:

   • The base of the triangle can be the segment between the second vertex (1, 7) and the third vertex (9, 7). The length of this base is: \[ 9 - 1 = 8 \text{ units} \]
   • The height of the triangle is the vertical distance from the first vertex (6, 1) to the line containing the base (y = 7). The height is: \[ 7 - 1 = 6 \text{ units} \]

4. Calculating the area of the triangle: The area \(A\) of a triangle is given by the formula: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \] Plugging in the base and height, we get: \[ A = \frac{1}{2} \times 8 \times 6 = \frac{48}{2} = 24 \text{ square units} \]

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