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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 50 paise per cm2.

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Solution

Given: Three sides of the triangular tiles are

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

It can be observed that

Semi-perimeter of each triangular-shaped tile, s=(35+28+9) cm2=36 cm

By Heron’s formula, we have

Area of triangle =s(sa)(sb)(sc)

Area of each triangular tile =36(3635)(3628)(369)

=[36×1×8×27] cm2

=[6×6×2×2×2×3×3×3] cm2

=6×2×32×3

=36×6

=(36×2.45) cm2 [6=2.45]

=88.2 cm2

Area of 16 tiles =(16×88.2) cm2=1411.2 cm2

Cost of polishing per cm2 area =50 paise

Cost of polishing 1411.2 cm2 area =Rs. (1411.2×0.50)=Rs. 705.60

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


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