The two trapezoids shown are similar. If the area of the larger trapezoid is 96 square centimeters, what is the area of the smaller trapezoid?
To find the area of the smaller trapezoid, we need to know the ratio of the areas of the larger and smaller trapezoids. Since the trapezoids are similar, their corresponding sides are proportional.
Let's assume the lengths of the corresponding bases of the larger and smaller trapezoids are B and b, respectively. Similarly, let's assume the heights of the trapezoids are H and h, respectively.
The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding sides. Therefore, the ratio of the areas of the larger and smaller trapezoids can be expressed as (B/b)^2.
Given that the area of the larger trapezoid is 96 square centimeters, we can set up the following equation:
(B/b)^2 = 96
Now, we need additional information to solve this equation. Specifically, we need either the lengths of the corresponding bases (B and b) or the ratio of their lengths.
If you have any additional information, such as the lengths of the bases or the ratio of their lengths, please provide it so that we can compute the area of the smaller trapezoid.