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