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In figure, A B C D is a field in the for...

In figure, `A B C D` is a field in the form of a quadrilateral whose sides are indicated in the figure. If `/_D A B=90^0,` Find the area of the field.

Text Solution

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`DeltaDAB` is a right angled triangle, therefore
`DB^(2)=DA^(2)+AB^(2)`
`DB^(2)=9^(2)+40^(2)`
`DB=sqrt(81+1600)m=sqrt(1681)m`
`DB=41 m`
`DeltaDAB` is right angled at A.
`:. `Area `(A_(1))=(1)/(2)xx9xx40=180 m^(2)`
In `DeltaDCB`, we have 2s=DC+CB+BD
`2s=28+15+41=84rArr s=42`
`:. A_(2)=` Area of `DeltaDCB`
`=sqrt(42xx(42-28)xx(42-15)xx(42-41))m^(2)`
`=sqrt(42xx14xx27xx1)`
`=sqrt(7xx2xx3xx7xx2xx3xx3xx3 m^(2)`
`=sqrt(7^(2)xx2^(2)xx3^(4)) m^(2)=(7xx2xx3^(2)) m^(2)=126 m^(2)`
Hence, area of the field `= A_(1)+A_(2)`
`=(180+126)m^(2)=306 m^(2)`.
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