Find the area of a quadrilateral one of whose diagonals is 40 cm and the lengths of the perpendiculars drawn from the opposite vertices on the diagonal are 16 cm and 12 cm.
Given : A quadrilateral
Diagonal AC = 40 cm
Perpendiculars to diagonal AC are: BL = 16 cm and DM = 12 cm
Now,
Area (quad. ABCD) = area (ABC) + area (ADC)
Area of triangle = × (base) × (height).
Therefore
Area of quad ABCD = × (AC) × (BL) + × (AC) × (DM)
= × (40) × (16) + × (40) × (12) = 320 + 240 = 560 cm2
Therefore area of the quadrilateral ABCD is 560 cm2.