.The diagonal of a quadrilateral shaped field is 32 m and the perpendiculars dropped on it from the remaining opposite vertices are 10m and 14m. Find the area of the field.

Area of the field = 384

Step-by-step explanation:

Given:

diagonal  = d = 32 m

perpendiculars dropped on it from the remaining opposite vertices:

h1 = 10 m

h2 = 14 m

Sum of perpendiculars:

h1 + h2 = 10  + 14

           = 24

Area of the field = 1/2 x d x (h1 + h2)

                           = 0.5(32)(24)

Area of the field = 384 m²