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Mensuration

Question
CBSEENMA8003446
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Find the length of the diagonal BD when, the area of the quadrilateral is 32 cm2.

Solution

Let the length of the diagonal BD = x cm
Area of the quadrilateral ABCD = 32 cm2
∵    Area of the quadrilateral  = 1 half x (A diagonal) x (Sum of the length of the perpendicular on the diagonal from the opposite vertices)
∴    Area of the quadrilateral ABCD = 1 half cross times BD cross times left parenthesis AP plus CQ right parenthesis
                                                        = 1 half cross times space straight x space cm cross times space left parenthesis 4.5 space cm space plus space 3.5 space cm right parenthesis

 
                                                        = 1 half cross times straight x cross times 8 space cm squared
Since area of the quadrilateral ABCD = 32 cm2
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                                                       = 8 cm
   Thus, the required length of the diagonal BD = 8 cm.

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