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Question
A quadrilateral field of unequal has a longer diagonal with 140m. The perpendiculars from opposite vertives upon this diagonal are 20m and 14m. Find the area of the field.
Solution
In quadrilateral ABCD, the sides AB, BC, CD and AD are unequal.
The longer diagonal BD = 140m
AM ⊥ BD, CL ⊥ BD
AM = 20m and CL = 14m.
We split a quadrilateral into triangles and find its area.
We know that,
Area of a Triangle = `(1)/(2)"b.h" "i.e" (1)/(2)("Base" xx "Height")`
Ar(ΔABD) = `(1)/(2)"BD" xx "AL";(Δ"CBD") = (1)/(2)"BD" xx "CM"`
Ar(QuadABCD) = Ar(ΔABD) + Ar(ΔCBD)
= `(1)/(2)"BD" xx "AL" + (1)/(2)"BD" xx "CM"`
= `(1)/(2)"BD" xx ("AL" + "CM")`
= `(1)/(2) xx 140 xx (20 + 14)`
= 70 x 34
= 2380m2.
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