Question

In trangle ABC MNII BC the Area of
Quadri lateral MBCN is 130 sqr. if AN: NC
4:5 then trangle MAN IS.​

Answer 1

Area of ΔMAN  = 32 sq units

Step-by-step explanation:

AN/NC = 4/5

AC = AN + NC

=> AN/AC  = 4/(4 + 5) = 4/9

MN ║ BC

=> ΔAMN ≈ ΔABC

=> Area of ΔAMN / Area of ΔABC =  (AN/AC  )²

=> Area of ΔAMN / Area of ΔABC =  (4/9 )²

=> Area of ΔAMN / Area of ΔABC =  16/81

=> Area of ΔABC = 81 * Area of ΔAMN/16

Area of Quadrilateral MBCN  = Area of ΔABC  -  Area of ΔAMN

=> 81 * Area of ΔAMN/16 - Area of ΔAMN  = 130

=> 65Area of ΔAMN  =  16 * 130

=> Area of ΔAMN  = 32 sq units

=>  Area of ΔMAN  = 32 sq units

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