Question

A floral design on a floor is made up of 16 tiles which are triangular ,the side of the triangle being 9 cm ,28 cm and 35 cm. Find the cost of polishing the tiles at the rate of 50p per cm square

Answer 1

Sides of one tile = 9 cm, 28 cm, 35 cm
Area of one tile, using Heron's formula
$S=\frac{9+28+35}{2}=\frac{72}{2}=36$
$\therefore A=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{36\times (36-9)\times (36-28)\times (36-35)}=\sqrt{36\times 27\times 8\times 1}=6\sqrt{3^3\times 2^3}=6\times 3\times 2\sqrt{6}=36\sqrt{6}c{m}^2$
$\therefore$ Area of 16 tiles $=16\times 36\sqrt{6}c{m}^2$
Cost of polishing $=50p/c{m}^2=0.5Re/c{m}^2$
Total amount $=0.5\times 16\times 36\sqrt{6}$
$=Rs.705.326$