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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
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 `underlinebb(1/2(h_1 + h_2)d)`.
Explanation:
Let ABCD be a quadrilateral, where h1 and h2 are altitudes on the diagonal BD = d.
Then, area of quadrilateral ABCD = `1/2(h_1 + h_2) xx BD`
If altitudes are halved and the diagonal is doubled, then
Area of quadrilateral ABCD = `1/2(h_1/2 + h_2/2) xx 2d`
= `1/2((h_1 + h_2)/2) xx 2d`
= `1/2(h_1 + h_2) xx d`
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