In a four sided field, the length of the longer diagonal is 128 m. The lengths of perpendiculars from the opposite vertices upon this diagonal are 22.7 m and 17.3 m. Find the area of the field.

Given:


BD = 128 m


CF = 22.7 m


AE = 17.3 m



Now,


In ∆ABD,


Area of a triangle = 1/2 × base × height


= 1/2 × BD × AE


= 1/2 × 128 × 17.3


= 1107.2 m2


Similarly,


In ∆CBD,


Area of a triangle = 1/2 × base × height


= 1/2 × BD × FC


= 1/2 × 128 × 22.7


= 1452.8 m2


Now,


Area of field = ∆ABD + ∆CBD


= 1107.2 m2 + 1452.8 m2


= 2560 m2


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