If the diagonal $d$ of a quadrilateral is doubled and the heights $h_{1}$ and $h_{2}$ falling on $d$ are halved, then the area of the quadrilateral is __________.

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Solution

Compute the area of the quadrilateral
Given: A quadrilateral with diagonal $d$ and heights $h_{1}$ and $h_{2}$ .
Thus, the area of the quadrilateral $= \frac{1}{2} (h_{1} + h_{2}) d$ $[A = \frac{1}{2} (s u m o f h i g h t s) d i a g o n a l]$
Since the diagonal is doubled and the heights are halved, we will get
Area of the new quadrilateral $= \frac{1}{2} (\frac{h_{1}}{2} + \frac{h_{2}}{2}) 2 d$
Area of the new quadrilateral $= \frac{1}{2} (h_{1} + h_{2}) d$
Hence, the area of the new quadrilateral is $\frac{1}{2} (h_{1} + h_{2}) d$ (the same as the original quadrilateral).

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If the diagonal d of a quadrilateral is doubled and the heights h1 andh2 falling on d are halved, then the area of the quadrilateral is __________.

If the diagonal $d$ of a quadrilateral is doubled and the heights $h_{1}$ and $h_{2}$ falling on $d$ are halved, then the area of the quadrilateral is __________.