RS Aggarwal & V Aggarwal - Mathematics

Book: RS Aggarwal & V Aggarwal - Mathematics

Chapter: 7. Areas

Subject: Mathematics - Class 9th

Q. No. 19 of Exercise 7A

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19

Find the perimeter and area of the quadrilateral ABCD in which AB = 17cm, AD = 9cm, CD = 12cm, =900 and AC = 15cm.

By using Pythagoras theorem in right triangle ABC, we get


BC=


=


=


=


= 8 cm


Let us first find out the perimeter of the given quadrilateral


Perimeter of quadrilateral ABCD = 17 + 9 + 12 + 8 = 46 cm


We know that,


Area of triangle ABC =


=


=


= 60 cm2


Now,


For area of triangle ACD, we have


a = 15 cm


b = 12 cm


And,


c = 9 cm


Therefore,


s =


=


= 18 cm


Now,


Area of triangle ACD =


=


=


=


= 18 × 3


= 54 cm2


Therefore,


Area of quadrilateral ABCD = Area of triangle ABC + Area of triangle ACD


= 60 + 54


= 114 cm2


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