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,
\(s = \frac{a + b + c}{2}\)
\(\therefore \) \(s = \frac{9 + 28 + 35}{2} = \frac{72}{2} = 36cm\)

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

= \(\sqrt{36 × 27 × 8 × 1}\)
= \(\sqrt{6 × 6 × 9 × 3 × 4 × 2 × 1}\)
= \(6 × 3 × 2\sqrt{6} {cm}^2\)
= \(36\sqrt{6} {cm}^2\)
\(\therefore \) 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