Square and rhombus on the same base (and between the same parallels)\nIf a square and a rhombus stand on the same base and between the same parallels, what is the ratio of their areas?

Introduction / Context:
The classical result “on the same base and between the same parallels” implies equal heights to that base. Figures with the same base and equal height have equal areas (Area = base * height for all parallelogram-type figures).

Given Data / Assumptions:

• Square and rhombus share the same base segment.
• Both lie between the same pair of parallels ⇒ same altitude to that base.

Concept / Approach:
Area(square) = base * common height. Area(rhombus) = base * the same common height. Hence, areas are equal.

Step-by-Step Solution:

Verification / Alternative check:
This mirrors the familiar result for triangles and parallelograms on the same base and between the same parallels; equality of heights forces equal areas.

Why Other Options Are Wrong:
Any ratio other than 1:1 contradicts the shared base and equal height condition.

Common Pitfalls:
Overlooking the phrase “between the same parallels” (often assumed) may lead to thinking the areas must differ; that phrase is essential for equality.

Final Answer:
1:1