Question

A floral design on a floor is made up of 16 tiles, each triangular in shape having sides 16 cm, 12 cm and 20 cm. Find the cost of polishing the tiles at Re 1 per sq cm.

Answer 1

Area of one triangular-shaped tile can be found in the following manner:

$$\begin{gathered} \mathrm{Let}: \\ a=16\mathrm{cm},b=12\mathrm{cm}\mathrm{and}c=20\mathrm{cm} \\ s=\frac{a+b+c}{2}=\frac{16+12+20}{2}=24\mathrm{cm} \\ \mathrm{By}\mathrm{Heron}\text{'}\mathrm{s}\mathrm{formula},\mathrm{we}\mathrm{have}: \\ \mathrm{Area}\mathrm{of}\mathrm{triangle}=\sqrt{s(s-a)(s-b)(s-c)} \\ =\sqrt{24(24-16)(24-12)(24-20)} \\ =\sqrt{24\times 8\times 12\times 4} \\ =\sqrt{6\times 4\times 4\times 4\times 4\times 6} \\ =6\times 4\times 4 \\ =96{\mathrm{cm}}^2 \end{gathered}$$

Now,
Area of 16 triangular-shaped tiles = $16\times 96=1536{\mathrm{cm}}^2$
Cost of polishing tiles of area 1 cm² = Rs 1
Cost of polishing tiles of area 1536 cm² = $1\times 1536=\mathrm{Rs}1536$