Question

A floor of a building consists of 2,500 tiles. All the tiles are rhombus shaped with diagonal 40 cm and 25 cm. Find the total cost of polishing the floor at the rate of ₹8 per square meter.​

Answer 1

$\star \; {\underline{\boxed{\pmb{\green{\frak{ \; Given \; :- }}}}}}$

• No. of Tiles = 2500
• Diagonals of the Tiles = 40 cm × 25 cm
• Rate of Polishing = Rs.8

$\star \; {\underline{\boxed{\pmb{\pink{\frak{ \; To \; Find \; :- }}}}}}$

• Cost of Polishing = ?

$\\ \qquad{\rule{200pt}{2pt}}$

$\star \; {\underline{\boxed{\pmb{\red{\frak{ \; SolutioN \; :- }}}}}}$

$\maltese$ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ Area{\small_{(Rhombus)}} = \dfrac{1}{2} \times D_1 \times D_2 }}}}}$

Where :

• $\sf{ D_1 }$ = Diagonal 1
• $\sf{ D_2 }$ = Diagonal 2

$\maltese$ Calculating the Area :

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { Area = Area \; of \; tiles \times No. \; of \; Tiles } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { Area = \bigg\{ \dfrac{1}{2} \times \bigg( D_1 \times D_2 \bigg) \bigg\} \times No. \; of \; Tiles } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { Area = \bigg\{ \dfrac{1}{2} \times \bigg( 40 \times 25 \bigg) \bigg\} \times 2500 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { Area = \bigg( \dfrac{1}{2} \times 1000 \bigg) \times 2500 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { Area = \bigg( \dfrac{1}{\cancel2} \times \cancel{1000} \bigg) \times 2500 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { Area = 1 \times 500 \times 2500 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { Area = 500 \times 2500 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; {\underline{\boxed{\pmb{\sf{ Area \; of \; Floor = 1250000 \; {cm}^{2} }}}}} \; {\red{\pmb{\bigstar}}} \\ \\ \\ \end{gathered}$

$\maltese$ Calculating the Cost :

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { Cost = Area \times Rate } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { Cost = 1250000 \times 8 } \qquad \; \bigg\lgroup {\purple{\sf{ 1 \; m = 100 \; cm }}} \bigg\rgroup \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { Cost = \dfrac{1250000}{100} \times 8 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { Cost = \cancel\dfrac{1250000}{100} \times 8 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { Cost = 12500 \times 8 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; {\underline{\boxed{\pmb{\sf{ Cost \; of \; Polishing = Rs. \; 100000 }}}}} \; {\green{\pmb{\bigstar}}} \\ \\ \\ \end{gathered}$

$\therefore \;$ Cost of Polishing the floor is Rs.100000 .

$\\ \qquad{\rule{200pt}{2pt}}$

Answer 2

No. of Tiles = 2500

Diagonals of the Tiles = 40 cm × 25 cm

Rate of Polishing = Rs.8

\begin{gathered} \\ \\ \end{gathered}