It is given that,

Length of the diagonal, d = 24 m

Length of the perpendiculars, h_{1 }and h_{2}, from the opposite vertices to the diagonal are h_{1} = 8 m and h_{2} = 13 m

Area of the quadrilateral = 1/2d (h_{1} + h_{2})

Thus, the area of the field is 252 m^{2}