A design is made on a rectangular tile of dimensions `"50 cm" xx "70 cm"` as shown in figure. The design shows `8` triangle, each of sides `26` `cm`, `17` `cm` and `25` `cm`. Find the total area of the design and the remaining area of the tiles.

Explanation

Given, the dimension of rectangular tile is `"50 cm" xx "70cm."`
`therefore"Area of rectangular tile" =50xx70=3500cm^(2)`
The sides of a design of one triangle be
a=25cm, b=17cm and c=26 cm.
`"Now, semi-perimeter, "s=(a+b+c)/(2)=(25+17+26)/(2)=(68)/(2)=34`
`therefore " ""Area of one triangle"=sqrt(s(s-a)(s-b)(s-c))" "["by Heron's formula"]`
`=sqrt(34xx9xx17xx8)`
`=sqrt(17xx2xx3xx3xx17xx2xx2xx2)`
`=17xx3xx2xx2=204cm^(2)`
`therefore"Total area of eight triangles"=204xx8=1632cm^(2)`
`"Now,"" ""area if tge desugb = Total area of eigfht triangles"`
`1632cm^(2)`
`"Also, remaining area of the tile = Area of the rectangle-Area of the design"`
`=3500-1632`
`=1868cm^(2)`
`"Hence, the total area of the design is 1632" cm^(2) "and the remaining area of the tile is 1868" cm^(2)`