ABCD is a quadrilateral. The length of the diagonal AC is 24 cm. The sum of the perpendicular drawn from vertex B and D on the diagonal AC is 10 cm. What is the area of the quadrilateral in cm²?

120

d = 24cm

h₁ + h₂ = 10cm

Area(Quadrilateral) = 1/2 x (h1 + h₂) x d

here,

d = diagonal

(h1 + h2) = sum of heights

Let's put the given values in the above formula,

Area(Quadrilateral) = 1/2 x (h1 + h2) x d = 1/2 x 10 x 24 = 120