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Question
The diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. Find the area of the field.
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Solution
It is given that,
Length of the diagonal, d = 24 m
The lengths of the perpendiculars, h1 and h2, from the opposite vertices to the diagonal are h1 = 8 m and h2 = 13 m
Area of the quadrilateral = `1/2` d(h1 + h2)
= `1/2` (24m) × (13m + 8cm)
= `1/2` (24 m) (21 m)
= 252 m2
Thus, the area of the field is 252 m2
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