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Question
A field is in the shape of a quadrilateral ABCD in which side AB = 18 m, side AD = 24 m, side BC = 40m, DC = 50 m and angle A = 90°. Find the area of the field.
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Solution
Since ∠A = 90°
By Pythagorus Theorem,
In ∆ABD,
Now, the area of ΔABD = `1/2 (18)(24)`
= (18) (12) = 216 m2
In ΔABD
BD = `sqrt("AB"^2 + "AD"^2) = sqrt(18^2 + 24^2)`
= `sqrt(324 + 576) = sqrt(900) = 30`m.
S = `120/20 = 60 cm^2`
=`sqrt( 60xx10xx20xx30)`
= `sqrt(10xx2xx3xx10xx10xx2xx10xx3)`
= 10 × 10 × 6
= 600 cm2
Area of quadrilateral ABCD
= 816cm2
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