Q7 of 83 Page 351

BD is one of the diagonals of a quad. ABCD. If AL ⊥ BD and CM ⊥ BD, show that ar(quad. ABCD) = x BD x (AL + CM).

Given :


AL ⊥ BD and CM ⊥ BD


To prove : ar (quad. ABCD) = x BD x (AL + CM)


Proof:


Area of ABD = x BD x AM


Area of ABD = x BD x CM


Now area of Quad ABCD = Area of ABD + Area of BCD


= x BD x AL + x BD x CM


= x BD x (AL + CM)


Hence proved


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