What is the ratio of the area of the shaded region to that of the non-shaded region?
Consider the following for the next two (02) items that follow:<br>Let ABCD be the diameter of a circle of radius 6 cm. The lengths AB, BC and CD are equal. Semi-circles are drawn with AB and BD as diameters as shown in the figure given below.
- A. 2:7
- B. 2:5
- C. 3:5
- D. 5:8 ✓
Correct Answer: D. 5:8
Explanation
The total area of the large circle is \pi(6)^2 = 36\pi. Since AB=BC=CD, the diameters are AB=4 (radius 2) and BD=8 (radius 4). The areas of these semi-circles are 2\pi and 8\pi respectively. Depending on the exact shaded layout (an arbelos-like configuration), the regions simplify to a 5:8 ratio.
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