Question

Three white squares overlap the cyan square such that one of their corners meet at the centre of the cyan square as shown in the figure. What is the ratio of the area of the shaded portion to the original cyan square?

• A. 45297
• B. 45295
• C. 45294
• D. 45359

Answer 1

The Correct Option is B

To solve this problem, we need to determine the ratio of the shaded area to the area of the original cyan square based on the given arrangement. Let's proceed with the steps:

1. Assume the side length of the cyan square is \(s\). Therefore, the area of the cyan square is:

\[ A_c = s^2 \]

2. There are three white squares overlapping the cyan square, and each has a corner at the center of the cyan square. If each white square has side length \(s/2\) (since this is a common configuration for such problems), the area of one white square would be:

\[ A_w = \left(\frac{s}{2}\right)^2 = \frac{s^2}{4} \]

3. The combined area of the three white squares is:

\[ A_{3w} = 3 \times \frac{s^2}{4} = \frac{3s^2}{4} \]

4. The shaded area is the part of the cyan square not covered by any white square. Therefore, the shaded area is:

\[ A_{shaded} = A_c - A_{3w} = s^2 - \frac{3s^2}{4} = \frac{s^2}{4} \]

5. The required ratio of the area of the shaded portion to the original cyan square is calculated as:

\[ \text{Ratio} = \frac{A_{shaded}}{A_c} = \frac{\frac{s^2}{4}}{s^2} = \frac{1}{4} \]

Therefore, the ratio of the shaded area to the area of the cyan square is \(\frac{1}{4}\). This matches with the correct answer, represented by option

45295

.