Question

the green (upper) triangle has an area of 6 inches². the purple (lower) triangle has an area of 6 inches². place the orange triangle (square symbols) directly next to the green triangle so that the two triangles together make a rectangle. the total area of this rectangle is , which is the area of the green triangle.

Explanation:

Step1: Recall rectangle - triangle area relationship

When two congruent right - angled triangles form a rectangle, the area of the rectangle is the sum of the areas of the two triangles.

Step2: Calculate the area of the rectangle

Since the green triangle has an area of 6 square inches and the orange triangle is congruent to the green one (to form a rectangle), the area of the rectangle $A = 6+6=12$ square inches.

Step3: Compare the rectangle and green - triangle areas

To find how the area of the rectangle relates to the area of the green triangle, we calculate the ratio $\frac{12}{6}=2$.

Answer:

The total area of this rectangle is 12 square inches, which is 2 times the area of the green triangle.