Question

The diagnol of a quadrilateral shaped field is 24 m and the perpendicular drops on it from the remaining opposite vertices are 8 m and 13 m. find the area of the feild

Answer 1

Area of upper triangle =1/2*b*
=1/2*13*24=12*13=156
Area of lower triangle =1/2*b*h
=1/2*24*8=24*4=96
Area of quadrilateral =area of upper +lower triangle =156+96=252

Answer 2

let the quadrilateral be ABCD and the perpendiculars be BE = 13 m and DF = 8 m. AC = 24 m.

in ∆ABC:
ar(∆) = ½b×h = ½×24×13 = 12×13 = 156 m²

in ∆ADC:
ar(∆) = ½b×h = ½×24×8 = 12×8 = 96 m²

total area of ABCD = 96 + 156 = 252 m²

therefore the area of the quadrilateral is 252 m²