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Question
A park, in the shape of a quadrilateral ABCD, has ∠C = 900, AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m How much area does it occupy?
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Solution
Given sides of a quadrilaterals are AB = 9, BC = 12, CD = 05, DA = 08
Let us joint BD
In ΔBCD applying Pythagoras theorem.
`BD^2=BC^2+CD^2`
=`(12)^2+(5)^2`
=144+25
=169
𝐵𝐷=13𝑚
Area of ΔBCD = `1/2`×𝐵𝐶×𝐶𝐷=[`1/2`×12×5]`m^2=30m^2`
or ΔABD
`S=sqrt(perimeter)/2=sqrt(9+8+13)/2=15cm`
By heron’s formula`sqrt(s(s-a)(s-b)(s-c))`
Area of the triangle =`sqrt(15(15-9)(15-8)(15-13))m^2`
=`35.496 + 30 m^2`
= `65.5 m^2` (approximately)
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