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 Fig. 12.18). Find the cost of polishing the tiles at the rate of `50 p"\ "p e r"\ "c m^2`.

Explanation

Given: Dimensions of the triangular tiles.
By using Heron’s formula, we can calculate the area of triangle.
Heron's formula for the area of a triangle, Area`=√s(s - a)(s - b)(s - c)`
Where `a`, `b` and `c` are the sides of the triangle, and `s=`Semi-perimeter`=`Half the Perimeter of the triangle`=(a+b+c)/2`
We have the dimensions of sides of each triangular tile.
`a=35 cm`, `b=28 cm`, `c=9 cm`
Semi Perimeter `(s)=(a+b+c)/2`
`s=(35+28+9)/2`
`s=72/2`
`s=36 cm`
By using Heron’s formula,
Area of each triangular tile`=sqrt(s(s - a)(s - b)(s - c))`
`=√36(36 - 35)(36 - 28)(36 - 9)`
`=sqrt(36×1×8×27)`
`=36sqrt(6) cm^2`
Area of a `1` triangular tile`=36sqrt(6) cm^2`
Area of `16` triangular tile`=16×36sqrt(6) cm^2`
`=16×36×2.45 cm^2`
`=1411.2 cm^2`
Since, the cost of polishing `1cm^2` of tiles is `50p` or `₹ 0.5`.
Therefore, the cost of polishing `1411.2 cm^2` area of tiles`=1411.2 cm^2×0.5=₹705.60`.