A design is made on a rectangular tile of dimensions `"50 cm" xx "17"` 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)`