Question

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 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, $s=\frac{(35+28+9)}{2}=36cm$

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

Area of each tile =
$\lfloor \sqrt{36(36-35)(36-28)(36-9)}\rfloor c{m}^2=\lfloor \sqrt{36\times 1\times 8\times 27}\rfloor c{m}^2=36\sqrt{6}c{m}^2=(36\times 2.45)c{m}^2=88.2c{m}^{2}Areaof16tiles=(16\times 88.2)c{m}^2=1411.2c{m}^{2}Costofpolishingperc{m}^{2}area=50pCostofpolishing1411.2c{m}^{2}area=Rs(1411.2\times 0.5)=Rs.705.6$

Therefore, it will cost Rs. 705.6 to polish all the tiles.