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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.
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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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