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Question

Find the area of a quadrilateral ABCD in which AD = 24 cm, BAD=900 and BCD forms an equilateral triangle whose each side is equal to 26 cm. (Take 3=1.73)

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Solution

In quadrilateral ABCD, AD = 24 cm, BAD=900


BCD is an equilateral triangle with side 26 cm
In right ΔABD,
BD2=AB2+AD2
(26)2=AB2+(24)2
676=AB2+576
AB2=676576=100=(10)2
AB = 10 cm
Now area of right ΔABD,
= 12base×altitude=12×10×24
= 120cm2
and area of equilateral ΔBCD with side 26 cm
= 34×(side)2=1.734×26×26cm2
= 292.37 cm2
Total area of a quadrilateral ABCD,
= 120+292.37cm2=412.37cm2


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