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 figure). Find the cost of polishing the tiles at a rate of 50 paise per cm².

Answer 1

The sides of a triangular tile in floral design are 9 cm, 28 cm and 35 cm respectively.

Semi-perimeter of triangular tile (s) 

= \(\frac { 9+28+35 }{ 2 }\) = \(\frac { 72 }{ 2 }\) = 36 cm

Area of a triangular tile by using Heron’s formula

Total area of such 16 tiles in a floral design

= 16 x 36√6

= 576√6

= 576 x 2.45 cm² [√6 = 2.45 approximate]

= 1411.20 cm² approximate

Cost of polishing the tile = 50 paise/cm²

Cost of polishing the 1411.20 cm² 

= Rs 1411.20 x \(\frac { 1 }{ 2 }\) 

= Rs 705.60.