To determine the area of the given non-right triangle, we will use the formula for the area of a triangle, which is:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
First, we identify the base and the height of the triangle by carefully counting the number of squares on the grid.
1. **Base**: Examine the vertices located at (4, 10) and (7, 10). The base lies along the 10th row from column 4 to column 7.
- The length of the base is calculated by counting the columns between these two points (7 - 4) which is 3 units.
2. **Height**: The height is the vertical distance from the vertex at (1, 2) to the 10th row (where the base lies).
- The height is calculated as the difference between the 10th row and the 2nd row (10 - 2) which is 8 units.
Using these values in the area formula:
\[ \text{Area} = \frac{1}{2} \times 3 \text{ units} \times 8 \text{ units} \]
\[ \text{Area} = \frac{1}{2} \times 24 \text{ square units} \]
\[ \text{Area} = 12 \text{ square units} \]
Therefore, the area of the non-right triangle is:
\[ \boxed{12 \text{ square units}} \]
Area of Non-right Triangles Quick Check
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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 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
28 square units
28 square units
14 square units
1 answer