Q. 26

Find the perimeter and area of the quadrilateral ABCD in which AB = 17 cm, AD = 9 cm, CD = 12 cm, ACB = 90° and AC = 15 cm.


Answer :

Given:


AC = 15 cm


AB = 17 cm


AD = 9 cm


CD = 12 cm


In ∆ACB (right-angled),


Base2 + Perpendicular2 = Hypotenuse2


BC2 + AC2 = AB2


BC2 = AB2 - AC2


BC2 = 172 - 152


BC2 = 289 - 225


BC2 = 64


BC= 8 cm


Area of ∆ACB = 1/2 × BC × AC


= 1/2 × 8 cm × 15 cm


= 60 cm2


In ∆ADC,


Area of ∆ADC = 1/2 × AD × CD


= 1/2 × 9 cm × 12 cm


= 54 cm2


Now,


Area of quadrilateral ABCD = Area of ∆ACB + Area of ∆ADC


= 60 cm2 + 54 cm2


= 114 cm2


And,


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


= 17 cm + 8 cm + 12 cm + 9 cm


= 46 cm


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