If the diagonal d of a quadrilateral

Question:

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 __________.

Solution:

½ (h1 +h2) d

Explanation:

Assume that ABCD be a quadrilateral, hand 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

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