If the diagonal d of a quadrilateral is doubled and the heights h1 and h2 falling on d are halved, then the area of quadrilateral is __________.
½ (h1 +h2) d
Assume that ABCD be a quadrilateral, h1 and h2 are the heights on the diagonal BD = d, then, the area of a quadrilateral be
= (1/2)(h1 +h2) BD
Since the diagonal is doubled and the heights are halved, we will get
= (1/2) [ (h1/2) +(h2/2) ] 2d
= ½ (h1 +h2) d