Re: AC and BD are diagonals of rectangle ABCD.
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01 Jul 2023, 23:24
OE
For the given rectangle, through the point of intersection of two diagonals AC and DB, draw a line parallel to AD and BC and draw a line parallel to AB and DC. Now, as these two lines are parallel to the horizontal and vertical lines of outer
rectangle, we can say that the outer rectangle ABCD has been divided into four smaller rectangles.
All four smaller rectangles have equal area. AO, BO, CO and DO are the diagonals of four smaller rectangles. Every diagonal AO, BO, CO and DO further divides area of rectangle into two equal parts. So, for every smaller rectangle area of shaded region is equal to area of unshaded region.
Based on this we can say area of total shaded region is equal to area of total unshaded region. Hence, Quantity A is equal to Quantity B because Quantity A is area of shaded portion and Quantity B is area of unshaded portion.
Ans. (C)