Explanation
Correct answer: 1681.
It’s given that trapezoid A and trapezoid B are similar. When two trapezoids are similar, the scale factor between their corresponding side lengths is , and the scale factor between their areas is . It’s given that the length of each side of trapezoid A is times the length of the corresponding side of trapezoid B, so the scale factor between their corresponding side lengths is . It follows that the scale factor between the areas is , or . Therefore, the area of trapezoid A is times as large as the area of trapezoid B.
Desmos solution:
Note: For similar figures, area scales by k^2, so square the side-length scale factor.
Enter in Desmos:
Reviewed and rewritten by CookSAT