Question

P 7. in centimetres. A Find the perimeter of the quadrilateral ABCD. 12 cm 8 cm E B 6 cm​

Answer 1

Step-by-step explanation

>>Find the area

Find the area and the perimeter of quadrilateral ABCD, if AB= 8 cm, AD= 10 cm, BD = 12 cm, DC = 13 cm, and ΔDBC=90∘  

Solution

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Area of the quadrilateral = area of the triangle ABD + area of the triangle DBC.

From ΔDBC, BC2=DC2−BD2     [Using Pythagoras theorem]

⟹BC2=132−122=25

⟹BC=25=5 cm

Area of the ΔDBC=21×b×h

=21×5×12

=30 cm2

Area of the ΔABD=s(s−a)(s−b)(s−c)

Here, s=210+12+8

=15 cm(1+root 7) cm²

∴  Area of the ΔABD

Answer 2

Answer: Area of the quadrilateral = area of the triangle ABD + area of the triangle DBC.

From ΔDBC, BC  

2

=DC  

2

−BD  

2

     [Using Pythagoras theorem]

⟹BC  

2

=13  

2

−12  

2

=25

⟹BC=  

25

​

=5 cm

Area of the ΔDBC=  

2

1

​

×b×h

=  

2

1

​

×5×12

=30 cm  

2

 

Area of the ΔABD=  

s(s−a)(s−b)(s−c)

​

 

Here, s=  

2

10+12+8

​

 

=15 cm

∴  Area of the ΔABD=  

15(15−10)(15−12)(15−8)

​

 

=15  

7

​

cm  

2

 

∴  area of the quadrilateral=15+15  

7

​

=15(1+  

7

​

) cm  

2