Question

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.

Answer 1

Given : A quadrilateral 

Diagonal AC = 40 cm 

Perpendiculars to diagonal AC are: BL = 16 cm and DM = 12 cm 

Now, 

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

Area of triangle = \(\frac{1}{2}\)× (base) × (height).

Therefore

Area of quad ABCD = \(\frac{1}{2}\)× (AC) × (BL) + \(\frac{1}{2}\)× (AC) × (DM)

= \(\frac{1}{2}\)× (40) × (16) + \(\frac{1}{2}\)× (40) × (12) = 320 + 240 = 560 cm²

Therefore area of the quadrilateral ABCD is 560 cm².