If the diagonal of a quadrilateral is doubled and the heights and falling on are halved, then the area of the quadrilateral is __________.
Compute the area of the quadrilateral
Given: A quadrilateral with diagonal and heights and .
Thus, the area of the quadrilateral
Since the diagonal is doubled and the heights are halved, we will get
Area of the new quadrilateral
Area of the new quadrilateral
Hence, the area of the new quadrilateral is (the same as the original quadrilateral).