Question

A design is made on a rectangular tile of dimensions 50 cm × 70 cm as shown in

Fig. 12.7. The design shows 8 triangles, each of sides 26 cm, 17 cm and 25 cm.

Find the total area of the design and the remaining area of the tile.

Answer 1

Answer:

The area of the rectangular tile=length×width=70×50=3500

The design  comprises of 8 congruent triangles with sides 17cm, 25cm &26cm.

According to Heron's formula the area(A) of triangle with sides a,b&c is given as

A=  2  

[s(s−a)(s−b)(s−c)]​  

where2s=(a+b+c).

Herea=17,b=25,c=26,s=  

2

(17+25+26)

​  

=  

2

68

=34

Area of each triangle

=  

2

 

[34×(34−17)(34−25)(34−26)]

​  

 

=  

2

 

(34×17×9×8)

​  

 

=  

2

 

(2×17×17×3×3×2×2×2)

​  

 

=2×2×3×17

=12×17

=204

So,the area of the total design=area of all 8 triangles=8×204=1632

And the remaining area of rectangular tile=3500−1632=1868

HOPE IT HELPS U MATE

Answer 2

Answer:

my handwriting isn't that great, but I hope it helps