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 4. The second vertex is at the top of row 9 and the right of column 4. The third vertex is at the top of row 6 and the right of column 9.
Find the area of the non-right triangle. The base and height are found by counting the squares.
(1 point)
Responses
32.5 square units
32.5 square units
17.5 square units
17.5 square units
35 square units
35 square units
65 square units
65 square units
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page 8 of 9
The correct answer is 35 square units.
To find the area of the triangle, we can divide it into two right triangles and a rectangle. The area of the rectangle is 10x5 = 50 square units. Since the triangle is half of the rectangle, the area of the triangle is 50/2 = 25 square units.
Next, we calculate the area of the right triangles by using the formula for the area of a triangle (base x height / 2).
For the right triangle on the left side, the base is 5 units and the height is 4 units, so the area is 5x4/2 = 10 square units.
For the right triangle on the right side, the base is 5 units and the height is 1 unit, so the area is 5x1/2 = 2.5 square units.
Adding all three areas together, we get 25 + 10 + 2.5 = 37.5 square units.