Q. 25

Find the area of the quadrilateral ABCD in which AD = 24 cm, BAD = 90° and ΔBCD is an equilateral triangle having each side equal to 26 cm. Also find the perimeter of the quadrilateral. [Give: √3 = 1.73.]


Answer :

Given:


BC = 26 cm


DC = 26 cm


AD = 24 cm


BD = 26 cm


In ∆BCD,




= 292.37 cm2


In ∆ADB,


Base2 + Perpendicular2 = Hypotenuse2


AB2 + AD2 = DB2


AB2 = DB2 - AD2


AB2 = 262 - 242


AB2 = 676 - 576


AB2 = 100


AB= 10 cm


Area of ∆ADB = 1/2 × AB × AD


= 1/2 × 10 cm × 24 cm


= 120 cm2


Now,


Area of quadrilateral ABCD = Area of ∆ADB + Area of ∆BCD


= 120cm2 + 292.37 cm2


= 412.37 cm2


And,


Perimeter of quadrilateral ABCD = AB + BC + CD + DA


= 10 cm + 26 cm + 26 cm + 24 cm


= 86 cm


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