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Question
Find the area of a quadrilateral ABCD in which AD = 24 cm, ∠BAD = 90° and BCD forms an equilateral triangle whose each side is equal to 26 cm. (Take √3 = 1.73)
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Solution
Given that, a quadrilateral ABCD in which AD = 24 cm, ∠BAD = 90°
BCD is equilateral triangle and sides BC = CD = BD = 26 cm
In ΔBAD By using Pythagoras theorem
`BA^2=BD^2-AD^2`
`⇒BA=sqrt(BD^2-AD^2)`
`=sqrt(676-576)`
`sqrt(100)=10cm`
𝐴𝑟𝑒𝑎 𝑜𝑓 Δ𝐵𝐴𝐷=`1/2`×𝐵𝐴×𝐴𝐷
=`1/2`×10×24
=`120cm^2`
𝐴𝑟𝑒𝑎 𝑜𝑓 Δ𝐵𝐶𝐷=`sqrt(a)/4xx(26)^2=292.37cm^2`
∴𝐴𝑟𝑒𝑎 𝑜𝑓 𝑞𝑢𝑎𝑑𝑟𝑖𝑙𝑎𝑡𝑒𝑟𝑎𝑙
ABCD = Area of ΔBAD + area of ΔBCD
= 120 + 292.37
= 412.37 `cm^2`
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