Question

The floor of a building consists of 3000 tiles which are rhombus shaped. The diagonals of each of the tiles are 45 cm and 30 cm. Find the total cost of polishing the floor, if cost per m² is Rs.25.

Answer 1

number of rhombus shaped tiles = 3000
length of 1st diagonal = 45cm
length of 2nd diagonal = 30cm

we know, area of rhombus = 1/2 × length of 1st diagonal × length of 2nd diagonal

so, area of each tile = 1/2 × 45 cm × 30 cm
= 45 × 15 cm² = 675 cm² = 675 × 10^-4 m²
= 0.0675 m² [ because 1m² = 10⁴ cm² ]

so, area of 3000 tiles = area of floor = 3000 × area of each tiles = 3000 × 0.0675 = 202.5 m²

given, rate of polishing floor = 25 Rs./m²
so, total cost of polishing floor = area of floor × rate of polishing floor
= 202.5 × 25 Rs.
= 5062.5 Rs.

hence, total cost of polishing = 5062.5 Rs.

Answer 2

Let's simplify the question.

We know that area of a rhombus is equals to half of the product of its diagonal.

Therefore area of each Rhombus equal to (45 x 30)/2 = 675 cm².

Therefore area of 3000 tiles equal to 3000 x 675 = 2025000 cm².

Now the most important part is to convert the centimetre into metre so that we can directly compute the cost.

1 cm = 0.01m

or, 2025000 cm² = 2025000 x 0.0001 = 202.5m² [Ans].

The total cost of polishing the floor is rupees 25 x 202.5 = Rs 5062.5.