The area of quadrilateral ABCD in the given figure is

Options

A. `57 cm^(2)`
B. `108 cm^(2)`
C. `114 cm^(2)`
D. `195 cm^(2)`

Answer

C

Explanation

In right `triangleACD,AC^(2)=(AD^(2)-CD^(2))=(17)^(2)=(8)^(2) =(289-64)=225`.
`therefore AC = sqrt225` = 15 cm.
In right `triangleABC, BC^(2)=AC^(2)-AB^(2)=(15)^(2)=(9)^(2)=(225-81)=144.`
`therefore BC = sqrt144 = 12 cm`.
ar(quad. ABCD)=`ar(triangleACD)+ar(triangleABC)`
`=[(1)/(2)xx8xx15)+((1)/(2)xx12xx9)]cm^(2)=(60+54)cm^(2)=144cm^(2)`