In the adjoining figure, ABCD is a quadrilateral in which diag. BD = 14 cm. If AL ⊥ BD and CM ⊥ BD such that AL = 8 cm and CM = 6 cm, find the area of quad. ABCD.
Given
AL ⊥ BD and CM ⊥ BD
BD = 14 cm
AL = 8 cm
CM = 6 cm
Here,
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)
Area of quad ABCD = x BD x (AL + CM) = x 14 x (8 + 6) = 98cm2
Area of quad ABCD = 98cm2