Answer:
Hence, the area of each small red triangle is 1/8 square units.
Explanation:
Let's denote the base length and height of each small red and blue triangle as 'b' and 'h', respectively.
Since the large square has an area of 1 square unit, each side of the square has a length of 1. Therefore, the diagonal of the square (represented by the dotted line in the diagram) has a length of √2.
The diagonal segments divide the square into four equal-sized triangles, so each of these triangles has an area of (1/4) square units.
Let's focus on one of the triangles, which consists of a red and a blue triangle.
The total area of the triangle is (1/4) square units.
The area of the blue triangle can be calculated using the formula for the area of a triangle: (1/2) * base * height.
The base of the blue triangle is the side length of the large square, which is 1 unit.
Let's denote the height of the blue triangle as 'h_blue'.
Therefore, the area of the blue triangle is (1/2) * 1 * h_blue = (1/2) * h_blue square units.
Since the red and blue triangles have the same base length and height, the area of the red triangle is also (1/2) * h_blue square units.
Now, let's consider the larger triangle (consisting of a red and a blue triangle) again. The total area of this triangle is (1/4) square units.
We know that the area of the blue triangle is (1/2) * h_blue square units. Similarly, the area of the red triangle is also (1/2) * h_blue square units.
Therefore, the sum of the areas of the red and blue triangles in the larger triangle is (1/2) * h_blue + (1/2) * h_blue = h_blue square units.
Since the total area of the larger triangle is (1/4) square units, we have the equation:
h_blue = (1/4)
Therefore, the height of the blue triangle is (1/4) unit.
As the height of the red triangle is also equal to the height of the blue triangle, the area of the red triangle is:
Area of the red triangle = (1/2) * h_red = (1/2) * (1/4) = 1/8 square units.