The diagonal of a quadrilateral is 20 cm in length and the lengths of perpendiculars on it from the opposite vertices are 8.5 cm and 11.5 cm. The area of the quadrilateral is

Question

Philoid · Accepted Answer

Given : A quadrilateral

Diagonal AC = 20 cm

Perpendiculars to diagonal AC are: BL = 11.5 cm and DM = 8.5 cm

Now,

Area (quad. ABCD) = area (ABC) + area (ADC)

Area of triangle = × (base) × (height).

Therefore

Area of quad ABCD = × (AC) × (BL) + × (AC) × (DM)

= × (20) × (11.5) + × (20) × (8.5) = 115 + 85 = 200 cm²

Therefore area of the quadrilateral ABCD is 200 cm².