A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm and 35 cm (see the given figure). Find the cost of polishing the tiles at the rate of 50p per cm^{2}.

#### Solution

It can be observed that

Semi-perimeter of each triangular-shaped tile,

`s=(35+28+9)/2=36cm`

By Heron’s formula,

`"Area of triangle "=sqrt(s(s-a)(s-b)(s-c))`

`"Area of each tile "=[sqrt(36(36-35)(36-28)(36-9))]cm^2`

`=[sqrt(36xx1xx8xx27)]cm^2`

`=36sqrt6 cm^2`

= (36 x 2.45) cm^2

= 88.2 cm^{2}

Area of 16 tiles = (16 × 88.2) cm^{2}= 1411.2 cm^{2}

Cost of polishing per cm^{2} area = 50 p

Cost of polishing 1411.2 cm^{2} area = Rs (1411.2 × 0.50) = Rs 705.60

Therefore, it will cost Rs 705.60 while polishing all the tiles.