[tex]\large\underline{\sf{Solution-}}[/tex]
Given that,
- Length of wall = 6m = 6 × 100 = 600 cm
- Breadth of wall = 4m = 4 × 100 = 400 cm
So,
[tex]\rm \: Area_{(wall)} = Length \times Breadth \\ [/tex]
[tex]\rm \: Area_{(wall)} = 600 \times 400 \\ [/tex]
[tex]\rm\implies \:\boxed{ \rm{ \:Area_{(wall)} = 240000 \: {cm}^{2} \: }} \\ [/tex]
Now,
Side of square tile = 10 cm
So,
[tex]\rm \: Area_{(tile)} = {(side)}^{2} \\ [/tex]
[tex]\rm \: Area_{(tile)} = {10}^{2} \\ [/tex]
[tex]\rm\implies \:\boxed{ \rm{ \:Area_{(tile)} = 100 \: {cm}^{2} \: }} \\ [/tex]
Let assume that number of square tiles of size 10 cm required for decorating a wall 6m x 4m be n.
So,
[tex]\rm \: n \times Area_{(tile)} = Area_{(wall)} \\ [/tex]
[tex]\rm \: n \times 100 = 240000 \\ [/tex]
[tex]\rm\implies \:\boxed{ \rm{ \:n \: = \: 2400 \: }} \\ [/tex]
So, 2400 square tiles of size 10 cm required for decorating a wall 6m x 4m.
Further given that,
[tex]\rm \: Cost \: of \: 1 \: tile \: = \: Rs \: 2.50 \\ [/tex]
So,
[tex]\rm \: Cost \: of \: 2400\: tiles \: = 2400 \times 2.50 = \: Rs \: 6000 \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Additional Information :-
[tex]\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Base\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}[/tex]