Let ABCD be a trapezium whose vertices lie on the parabola \( y^2 = 4x \). Let the sides AD and BC of the trapezium be parallel to the y-axis. If the diagonal AC is of length \( \frac{25}{4} \) and it passes through the point \( (1, 0) \), then the area of ABCD is:
Show Hint
- \( \frac{125}{8} \)
- \( \frac{75}{8} \)
- \( \frac{25}{2} \)
- \( \frac{75}{4} \)
The Correct Option is B
Solution and Explanation
We are given the geometry of the trapezium and need to calculate its area.
Step 1: First, determine the coordinates of the vertices of the trapezium using the equation \( y^2 = 4x \).
Step 2: Calculate the length of diagonal AC by using the distance formula between the points.
Step 3: Use the area formula for a trapezium, which involves calculating the parallel sides' lengths and height, to find the area.
Final Conclusion: The area of ABCD is \( \frac{75}{8} \), which is Option 2.
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