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 3 and the right of column 3. The second vertex is at the bottom of row 10 and the left of column 1. The third vertex is at the bottom of row 10 and the right of column 10.
What is the area of the non-right triangle? The base and height are found by counting the squares.
(1 point)
The area is
square units.
The area is 42 square units.
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 6. The second vertex is at the top of row 8 and the right of column 1. The third vertex is at the top of row 10 and right of column 10.
What is the area of the non-right triangle? The base and height are found by counting the squares.
The area is 45 square units.
To find the area of the non-right triangle, we need to calculate the base and the height of the triangle. We can determine these by counting the number of squares from the given points.
First, let's identify the coordinates of the three vertices:
1. The first vertex is at the top of row 3 and the right of column 3: (3, 3)
2. The second vertex is at the bottom of row 10 and the left of column 1: (10, 1)
3. The third vertex is at the bottom of row 10 and the right of column 10: (10, 10)
Now, let's calculate the base and the height:
- The base is the horizontal distance between the second and third vertices, which is given by the difference in column numbers: 10 - 1 = 9 columns.
- The height is the vertical distance between the first vertex and the line connecting the second and third vertices. To find this, we need to count the number of rows from the first vertex to the line connecting the second and third vertices. In this case, we need to count the number of rows downwards from the first vertex until we reach the same row as the second and third vertices.
The first vertex is at row 3, and the line connecting the second and third vertices is at row 10. Therefore, the height is 10 - 3 = 7 rows.
Finally, we can calculate the area of the non-right triangle using the formula:
Area = 1/2 * base * height
Plugging in the values we obtained:
Area = 1/2 * 9 columns * 7 rows
= 1/2 * 63 square units
= 31.5 square units
Therefore, the area of the non-right triangle is 31.5 square units.