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 50p per cm²

We know that, Heron's formula

Area of triangle = $\sqrt{s (s - a) (s - b) (s -c)}$

where, s is the semi-perimeter = half of the perimeter

and  a, b and c are the sides of the triangle 

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 above formula, 

Area of each triangular tile = $\sqrt{s (s - a) (s - b) (s -c)}$

= $\sqrt{36(36 - 35)(36 - 28)(36 - 9)}$

= $\sqrt{36 \times 1 \times 8 \times 27}$

= 36$\sqrt{6}$ cm²

Area of a 1 triangular tile = 36$\sqrt{6}$ cm²

Area of 16 triangular tile = 16 $\times$ 36$\sqrt{6}$ cm²

= 16 $\times$ 36 $\times$2.45 cm²

= 1411.2 cm²

Since, the cost of polishing 1cm² of tiles is 50p or ₹ 0.5

Hence,  the cost of polishing 1411.2 cm² area of tiles = 1411.2 cm² $\times$0.5 

= ₹ 705.60