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.

Question

Philoid · Accepted Answer

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.