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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 50p per cm2.


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Solution


It can be observed that
Semi-perimeter of each triangular-shaped tile, s=(35+28+9)2=36 cm

By Heron’s formula,
Area of triangle = s(sa)(sb)(sc)

Area of each tile =
36(3635)(3628)(369)cm2=36×1×8×27cm2=366 cm2=(36×2.45) cm2=88.2 cm2Area of 16 tiles=(16×88.2) cm2=1411.2 cm2Cost of polishing per cm2 area=50 pCost of polishing 1411.2 cm2 area=Rs (1411.2×0.5)=Rs. 705.6

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

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