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To find the total cost of polishing the floor,

we first need to calculate the area of each rhombus-shaped tile.

The area of a rhombus can be calculated using the formula: Area = (diagonal1 × diagonal2) / 2.

For each tile, the area would be (45 cm × 30 cm) / 2 = 675 cm².

Now, we need to convert the area from cm² to m².

Since 1 m = 100 cm,

1 m² = 10000 cm².

Therefore, the area of each tile in m² would be 675 cm² / 10000

= 0.0675 m².

To find the total cost of polishing the floor, we multiply the area of each tile by the number of tiles (3000) and the cost per m² (Rs. 4).

Total cost = Area of each tile × Number of tiles × Cost per m²

Total cost = 0.0675 m² × 3000 × Rs. 4 = Rs. 810

Therefore, the total cost of polishing the floor would be Rs. 810.

Answer:

• Total Cost of polishing the floor is Rs. 810

Step-by-step explanation:

Given Information:

• The floor of a building consists of 3000 tiles
• Tiles are Rhombus in Shape
• Diagonals of each tile are 45cm and 30cm
• Cost of polishing the floor per m² = Rs. 4

Step 1: Finding the Area of One Tile:

We know that,

• Area of a Rhombus = 1/2 × d1 × d2

Where,

• d1 denotes diagonal 1
• d2 denotes diagonal 2

Substituting values in the Formula:

[tex] \\ \displaystyle \sf Area \: of \: one \: Tile = \frac{1}{ \cancel{2}} \times 45 \times \cancel{30} \: 15 \: \: \: \: \: \: \: \\ \\ \sf Area \: of \: one \: Tile = 1 \times 45 \times 15 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf Area \: of \: one \: Tile = 45 \times 15 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf Area \: of \: one \: Tile = 675 \: cm {}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]

• Area of one Tile is 675cm²

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Step 2: Finding the Area of 3000 tiles/ Area of the Floor:

Area of the Floor = 3000 × 675cm²

Area of the Floor = 2025000 cm²

• Area of the Floor is 2025000 cm².

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Step 3: Converting cm² into m²:

[tex] \\ \displaystyle \sf \longmapsto \: \: \bigg[2025000 \times \bigg( \frac{1}{100} \bigg) {}^{2} \bigg ] \: m {}^{2} \: \: \: \: \: \: \\ \\ \sf \longmapsto \: \: \bigg[2025000 \times \frac{1}{100} \times \frac{1}{100} \bigg] \: m {}^{2} \: \\ \\ \sf \longmapsto \: \: \bigg[ \frac{2025 \cancel{000}}{10 \cancel{000}} \bigg]\: m {}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \longmapsto \: \: \bigg[ \frac{2025}{10} \bigg ]\: m {}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \longmapsto \: \: \bigg[ \frac{1012.5}{5} \bigg] \: m {}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]

Removing decimal by dividing 1012.5 by 10

[tex] \\ \displaystyle \sf \longmapsto \: \: \bigg[\frac{1012 \cancel{.}5}{5 \times 10} \bigg ] \: m {}^{2} \\ \\ \sf \longmapsto \: \: \bigg [ \frac{10125}{50} \bigg ] \: m {}^{2} \: \\ \\ \bf \longmapsto \: \: 202.5 \: m {}^{2} \: \: \: \: \: \: [/tex]

• Area of the Floor in m² is 202.5m².

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Step 4: Finding the cost of polishing the floor:

Cost of Polishing the floor = 202.5 × Rs. 4

Cost of Polishing the floor = Rs. 810

• Hence, the Total cost of polishing the floor is Rs. 810

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