x BD2(AM + CN).In the given figure, ABCD is a quadrilateral. Prove tha – InterviewSolution

1.	x BD2(AM + CN).In the given figure, ABCD is a quadrilateral. Prove that ar(quadrilateral ABCD)where AM and CN are perpendiculars on diagonal BD22.
Answer» In∆ABD,AM is height and BD is baseArea of ∆ADB=1÷2×base×height=1÷2×AM×BD___(1)In ∆CBD,CN is height and BD is baseArea of ∆CBD=1÷2×base×height=1÷2×CN×BD___(2)AREA of ABCD=Area of ∆ADB+Area of CBD=1÷2×AM×BD+1÷2×CN×BD=1÷2×BD×(AM+CN)

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