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 50p per $c{m}^2$.

Answer 1

It can be observed that
Semi-perimeter of each triangular-shaped tile, $s=\frac{(35+28+9)}{2}=36m$

By Heron’s formula,
Area of triangle = $\sqrt{s(s-a)(s-b)(s-c)}$

Area of each tile = $\lfloor \sqrt{36(36-35)(36-28)(36-9)}\rfloor c{m}^2=\lfloor \sqrt{36\times 1\times 8\times 27}\rfloor c{m}^2=36\sqrt{6}c{m}^2=(36\times 2.45)c{m}^2=88.2c{m}^{2}Areaof16tiles=(16\times 88.2)c{m}^2=1411.2c{m}^{2}Costofpolishingperc{m}^{2}area=50pCostofpolishing1411.2c{m}^{2}area=Rs(1411.2\times 0.50)=Rs.705.60$

Therefore, it will cost Rs705.60 while polishing all the tiles.