Question

Q13.In the adjoining figure, find the area of the trapezium PQRS. 8 cm S MENTO R 17 cm P р Q 8 cm 78 cm​

Answer 1

Answer:

Solution

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Let us construct =DE ∣∣ CB

∴DC=EB=52 cm

 

DE=CB=30 cm

AE=AB−EB

=78−52=26 cm

For ΔADE,s=  

2

28+30+26

​

=42

ΔDAE is a scalene triangle

Area(ΔDAE)=  

s(s−a)(s−b)(s−c)

​

 

=  

42(42−30)(42−28)(42−26)

​

 

=  

42×12×14×16

​

 

=  

6×7×6×2×7×2×4×4

​

 

​

 

=  

6×6×7×7×2×2×4×4

​

 

=6×7×2×4

=336 cm  

2

 

But we know Area(ΔDAE)=  

2

1

​

×AE×Height

⇒336=  

2

1

​

×26×h

Area of trapezium ABCD=  

2

1

​

×h×(sum of parallel sides)

=  

2

1

​

×  

13

336

​

×130=1680 cm  

2

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