A floral design on a floor is made up of 16 tiles, each triangular in shape having sides 16 cm, 12 cm and 20 cm. Find the cost of polishing the tiles at Rs 1 per sq cm.

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Solution

Let, a = 16 cm, b = 12 cm and c = 20 cm

Now,

S = 1/2(a+b+c)

S = 1/2(16+12+20)=48/2=24cm

Area of one triangular tile =√S(S−a)(S−b)(S−c)

= √24(24−16)(24−12)(24−20)

= √2×2×2×2××2×2×2×2×2×2×3×3

= √2×2×2×2×2×3

Area of one tile = 96 $c m^{2}$

⇒ area of all tiles = 96×16=1536 $c m^{2}$

Cost of polishing the tiles per sq. cm = Re. 1

Thus, the total cost of polishing all the tiles = Rs. (1×1536)=Rs.1536

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