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Question

The diagonal of a quadrilateral shaped field is 24m and the perpendiculars dropped on it from the remaining opposite vertices are 8mand13m. Find the area of the field.

301293_4f41c067fd8c4be0ab12559bd54550ce.png

A
25.2m2
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B
252cm2
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C
272m2
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D
None of these
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Solution

The correct option is A 25.2m2
Let ABCD be the given quadrilateral in which BEACandDFAC.
It is given that
AC=24m,BE=8mandDF=13m.
Now, area of quad. ABCD=areaofΔABC+areaofΔACD
=12×AC×BE+12×AC×DF
=(12×8+12×13)m2
=(96+156)m2=252m2
290926_301293_ans.png

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