Question

Area of Non-right Triangles Quick Check
5 of 55 of 5 Items












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

24 square units
24 square units

28 square units
28 square units

12 square units
12 square units

14 square units
14 square units

Answer 1

pick one of the options

Answer 2

To find the area of the non-right triangle, you can divide the triangle into two right triangles and a rectangle in the middle. The base of each right triangle can be calculated by counting the number of squares from their common point (row 10, column 1) to their other points. The base of each right triangle is 3 units. The height of the right triangles will be 9 units.

So, the area of one right triangle is (1/2)*(3)*(9) = 13.5 square units. Since there are two right triangles, the total area of the right triangles is 2*13.5 = 27 square units.

The area of the rectangle in the middle can be calculated by counting the number of squares in its base and height. The base is 6 units and the height is 9 units.

So, the area of the rectangle is 9*6 = 54 square units.

The area of the non-right triangle is the sum of the areas of the right triangles and the rectangle: 27 + 54 = 81 square units.

Therefore, the correct answer is not provided in the options. The area of the non-right triangle is 81 square units.