Question

A floral design on a floor is made up of $16$ tiles which are triangular, the sides of the triangle being $9cm,28cm,$ and $35cm$ (see the given figure). Find the cost of polishing the tiles at the rate of $50$ paise per $c{m}^2.$

Answer 1

Given: Three sides of the triangular tiles are

$a=35cm,b=28cm,$ and $c=9cm$

It can be observed that

Semi-perimeter of each triangular-shaped tile, $s=\frac{(35+28+9)cm}{2}=36cm$

By Heron’s formula, we have

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

Area of each triangular tile $=\sqrt{36(36-35)(36-28)(36-9)}$

$=\left[\sqrt{36\times 1\times 8\times 27}\right]c{m}^2$

$=\left[\sqrt{6\times 6\times 2\times 2\times 2\times 3\times 3\times 3}\right]c{m}^2$

$=6\times 2\times 3\sqrt{2\times 3}$

$=36\times \sqrt{6}$

$=(36\times 2.45)c{m}^2$ [$\because \sqrt{6}=2.45$]

$=88.2c{m}^2$​

Area of $16$ tiles $=(16\times 88.2)c{m}^2=1411.2c{m}^2$

Cost of polishing per $c{m}^2$ area $=50$ paise

Cost of polishing $1411.2c{m}^2$ area $=Rs.(1411.2\times 0.50)=Rs.705.60$

Therefore, it will cost $Rs.705.60$ while polishing all the tiles.