In a four sider- 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 and Find the area of the field.

Explanation

Let ABCD be the field, and let AC be its longer diagonal.
Let BL `bot` AC and DM `bot` AC.
Then, AC = 128 m, BL = 22.7 m and DM = 17.3 m.
`therefore" ""area of the field"={(1)/(2) xx AC xx(BL+DM)}m^(2)`
`=[(1)/(2)xx 128 xx (22.7 + 17.3)]m^(2)`
`=(64 xx 40)m^(2) = 2560 m^(2)`.