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