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 area=35 cm,b=28 cm, and c=9 cm It can be observed thatSemi-perimeter of each triangular-shaped tile, s=(35+28+9) cm2=36 cmBy Heron’s formula, we haveArea of triangle =√s(s−a)(s−b)(s−c)Area of each triangular tile =√36(36−35)(36−28)(36−9) =[√36×1×8×27] cm2=[√6×6×2×2×2×3×3×3] cm2=6×2×3√2×3=36×√6=(36×2.45) cm2 [∵√6=2.45]=88.2 cm2​Area of 16 tiles =(16×88.2) cm2=1411.2 cm2Cost of polishing per cm2 area =50 paise Cost of polishing 1411.2 cm2 area =Rs. (1411.2×0.50)=Rs. 705.60Therefore, it will cost Rs. 705.60 while polishing all the tiles.

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