What is the area of the major segment?
Consider the following for the next two (02) items that follow:<br><br>A chord of length l of a circle makes an angle 90^\circ at the centre of the circle.
- A. \frac{l^{2}}{4}(\frac{3\pi}{2}+1) ✓
- B. \frac{l^{2}}{4}(\frac{3\pi}{2}-1)
- C. \frac{l^{2}}{2}(\frac{3\pi}{2}+1)
- D. \frac{l^{2}}{2}(\frac{3\pi}{2}-1)
Correct Answer: A. \frac{l^{2}}{4}(\frac{3\pi}{2}+1)
Explanation
The major segment area is the area of the major sector plus the area of the triangle. Area = \frac{270^\circ}{360^\circ}\pi r^2 + \frac{1}{2}r^2. Using r^2 = \frac{l^2}{2}, it becomes \frac{3\pi}{4}(\frac{l^2}{2}) + \frac{1}{2}(\frac{l^2}{2}) = \frac{l^2}{4}(\frac{3\pi}{2} + 1).
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