In the given figure, AC is a diagonal of quad. ABCD in which BL ⊥ AC and DM ⊥ AC. Prove that or (quad. ABCD)

Question

Philoid · Accepted Answer

Here we have ABCD as a quadrilateral with one of its diagonal as AC and BL and DM are perpendicular to AC

Thus, ar(ABCD) = ar(∆ADC) + ar(∆ABC)

Since, (BL ⊥ AC) and (DM ⊥ AC)

∴ Area of ABCD = ( ⨯ AC ⨯ BL) + ( ⨯ AC ⨯ DM)

= ⨯ AC ⨯ (BL + DM)