Question:medium

Find the ratio of area of shaded region in figure (i) to that of figure (ii).

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In area-ratio problems, if the radii and central angles are identical, the areas will always be equal regardless of the orientation of the figure.
Updated On: Feb 21, 2026
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Solution and Explanation

Understanding the Concept:
To compare two shaded regions, we first observe the geometrical shapes involved. The area of most plane figures depends on their dimensions. For example, the area of a circle is proportional to $r^2$, and similarly, other shapes also depend on their respective formulas. If two figures are constructed using the same measurements, their areas may turn out to be equal even if their orientation is different.

Method of Comparison:
1) Identify the formula for area of each figure.
2) Substitute the given dimensions into the formula.
3) Simplify both areas separately.
4) Take the ratio $\frac{Area_1}{Area_2}$ and reduce it to simplest form.

If both shaded regions are formed using identical dimensions and are merely arranged differently, their numerical areas will be equal.

Final Result:
The ratio of the two shaded areas = $1 : 1$.
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