Question

The floor of a building costs of 3000 tiles which are rhombus shaped and each of its diagonals are 45 cm and 30 cm in length. Find the total cost of polishing the floor of it costs per m² is ₹4

Answer 1

Answer

$\boxed{\boxed{\mathsf{Total\: Cost = 810rs}}}$

Step-by-step Explanation :

Given

• The floor of building consist of 3000 tiles each in rhombus shape

• Diagonals of rhombus are 45cm and 30cm.

• Rate of polishing per m^2 = 4rs

To find

• Total Cost of polishing the floor .

Solution

Now we know that

$\implies \mathsf{Area\: of\: Floor = Area\: of \: one\: Tile \times 3000}$

✓ Finding area of Floor

Now since it's given that the tiles are in the shape of Rhombus

Therefore we know that ,

$\boxed{\mathsf{\bigstar \: Area\: of \: Rhombus = \dfrac{1}{2} \times D_1 \times D_2}}$

Where here,

$\longrightarrow \: \mathsf{D_1 = Diagonal\: One = 45cm}$

$\longrightarrow \: \mathsf{D_2 = Diagonal\: two = 30cm}$

Therefore we have

$\longrightarrow \: \mathsf{Area\: of\: one\: tile = \dfrac{1}{2} \times (45cm) \times (30cm)}$

$\longrightarrow \: \mathsf{Area\: of\: one\: tile = \dfrac{1}{2} \times 1350{cm}^{2}}$

$\longrightarrow \: \mathbf{\mathsf{Area\: of\: one\: tile = 675{cm}^{2}}}$

Thus Now,

$\implies \: \mathsf{Area\: of\: floor = Area\: of \: one \: tiles \times Total \: no \: of \: tiles}$

$\longrightarrow \: \mathsf{Area\: of\: floor = 675{cm}^{2} \times 3000}$

$\longrightarrow \: \mathsf{Area\: of\: floor = 2025000{cm}^{2}}$

$\longrightarrow \: \mathbf{\mathsf{Area\: of\: floor = \dfrac{2025000{cm}^{2}}{10000} = 202.5{m}^{2}}}$

[As 1 m^2 = 10000 cm^2]

Therefore now Cost of Polishing

$\implies \mathsf{\:Cost \: polishing = Total\: area \times Rate\: of polishing}$

$\longrightarrow \mathsf{\:Cost \: polishing = 202.5{m}^{2} \times 4rs}$

$\longrightarrow \mathsf{\:Cost \: polishing = 810rs}$

Therefore we have required answer

$\underline{\boxed{\mathsf{Total\: Cost = 810rs}}}$

Answer 2

Given :-----

• 3000 tiles required in a floor...
• Diagonal of Rhombus = 45cm & 30 cm.
• cost of polishing the floor = Rs. 4 /m²

To Find :-----

• Total cost of polishing the floor ?

Formula used :-----

• Area of Diagonal = 1/2 × Diagonal 1 × Diagonal 2
• 10000cm² = 1m²

$\huge{\mathfrak{\green{S}}}{\mathfrak{o}}{\mathfrak{\orange{l}}}{\mathfrak{\red{u}}}{\mathfrak{\pink{t}}}{\mathfrak{\purple{i}}}{\mathfrak{\blue{o}}}{\mathfrak{\red{n}}}$ :---------

since diagonals of Rhombus Are Given as 45 cm and 30cm.

putting values in above formula we get,

$Area \: of \: Rhombus = \: \frac{1}{ \cancel2} \times \cancel 30 \times 45 \\ \\ Area \: of \: Rhombus = 675 {cm}^{2}$

Now, it is given that 3000 tiles are used in floor ,

Area of 1 tile = 675cm²

Area of 3000 tiles = 675 × 3000 = 2025000cm²

___________________

Now , we know that,

10000cm² = 1m²

so,

2025000cm² = 2025000/10000 = 202.5m²

so, Area to be polished of floor is 202.5m².

_____________________

Now, it is given that cost of Polishing the floor is = Rs4/m² .

so, cost of Polishing the floor of Area 202.5m² is = 4×202.5 = $\boxed{\boxed{\mathsf{Rs.\:810}}}$

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(Hope it Helps you)

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Extra Brainly knowledge :-----

1) Area of Rhombus = Side of Rhombus × Height

2) Diagonals of Rhombus bisect each other at 90°.

3) All sides of rhombus are equal in length and opposite sides are parallel to each other ...

4) perimeter of Rhombus = 4 × side ..