1. (10 points) If a square with a side length of 8 cm is placed over a triangle, then the area of the overlapping part of the two shapes is half of the triangle's area and three-quarters of the square's area. What is the area of this triangle? $\qquad$ square centimeters.
【Analysis】According to the area formula of a square $S=a \times a$ to find the area of the square, then based on "two-thirds of the square's area," find the area of the overlapping part of the two figures, and then find the area of the triangle.

【Solution】Solution: $8 \times 8 \times \frac{3}{4} \div \frac{1}{2}$,
$$
=48 \times 2 \text {, }
$$
$=96$ (square centimeters),
Answer: The area of this triangle is 96 square centimeters;
Therefore, the answer is: 96.