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 figure). Find the cost polishing the tiles at the rate of Rs.50 paise per ${cm}^{2}$.

Given,
the sides of a triangular tile are 9 cm, 28 cm and 35 cm.

For each triangular tile, we have,
$s=\frac{a+b+c}{2}$
$?$ $s=\frac{9+28+35}{2}=\frac{72}{2}=36cm$

Now, Area of triangle
= $\sqrt{36\left(36?9\right)\left(36?28\right)\left(36?35\right)}$
(Since, Heron's formula [area = $\sqrt{s\left(s?a\right)\left(s?b\right)\left(s?c\right)}$])

= $\sqrt{36×27×8×1}$
= $\sqrt{6×6×9×3×4×2×1}$
= $6×3×2\sqrt{6}{cm}^{2}$
= $36\sqrt{6}{cm}^{2}$
$?$ Total area of 16 such titles
= 16 × $36\sqrt{6}$
= 16 × 36 × 2.45 ${cm}^{2}$ = 1411.20 ${cm}^{2}$

Total cost of ploshing the titles at the rate of Rs.50 paise per ${cm}^{2}$
= Rs. $\frac{50}{100}×1411.20$ = Rs.705.60