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 __________.

Question

Fill in the blanks to make the statement true.

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 __________.

Answer 1

½ (h₁ +h₂) d

Explanation:

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