Appropriate Question :-

A room is 8.5 m long, 7m wide and 4m height. it has one door measuring 1m by 1m and two windows each measuring 0.5m by 0.5 m. Find the cost of painting its four walls without door and windows. If the rate of painting is ₹ 2 per square metre.

[tex]\large\underline{\sf{Solution-}}[/tex]

Given that,

• A room is 8.5 m long, 7m wide and 4m height.

• Room has one door measuring 1 m by 1 m.

• Room has two windows each measuring 0.5 m by 0.5 m.

So,

[tex]\rm \: Area_{(To\:be\:painted)} \\ [/tex]

[tex]\rm \: = \: Area_{(4\:walls)} - Area_{(1\:door)} - Area_{(2\:window)} \\ [/tex]

[tex]\rm \: = 2(8.5 + 7) \times 4 - 1 \times 1 - 2 \times (0.5 \times 0.5) \\ [/tex]

[tex]\rm \: = 2 \times 15.5 \times 4 - 1 - 2 \times 0.25 \\ [/tex]

[tex]\rm \: = 31 \times 4 - 1 - 0.50 \\ [/tex]

[tex]\rm \: = 124 - 1.5 \\ [/tex]

[tex]\rm \: = 122.5 \\ [/tex]

[tex]\rm\implies \:Area_{(To\:be\:painted)} = 122.5 \: {m}^{2} \\ [/tex]

Now,

Cost of white washing 1 m² = ₹ 2

So,

Cost of white washing 122.5 m² = 122.5 × 2 = ₹ 245

[tex]\rule{190pt}{2pt}[/tex]

Formulae Used :-

Area of four walls of length l, breadth b and height h is given by

[tex]\boxed{ \rm{ \:Area_{(4\:walls)} \: = \: 2 \times (l + b) \times h \: \: }} \\ [/tex]

Area of rectangle of length l and breadth b is given by

[tex]\boxed{ \rm{ \:Area_{(rectangle)} \: = \: l \times b \: \: }} \\ [/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]

[tex]{\large{\underline{\pmb{\sf Given:-}}}}[/tex]

• Dimensions of room = 8.5 m × 7 m × 4 m
• Dimension of door = 1 m × 1 m
• Dimension of one window = 0.5 m × 0.5 m

[tex]{\large{\underline{\pmb{\sf To\;Find :-}}}}[/tex]

Cost of painting its four walls without door and windows, if the rate of painting is ₹ 2 per square metre.

[tex]{\large{\underline{\pmb{\sf Solution:-}}}}[/tex]

At first we need to find the area of four walls

[tex]{\large{\boxed{\underline{\underline{\underline{\red{\bf Area\;of\;4\;walls\;=2(l+b)\times h}}}}}}} \bigstar[/tex]

[tex]\sf :\implies Area=2(8.5 + 7)\times 4[/tex]

[tex]\sf :\implies Area = 2(15.5)\times 4[/tex]

[tex]\sf :\implies Area = 31\times 4[/tex]

[tex]\sf :\implies Area = 124 \;m^2[/tex]

Now since door and window are in the shape of square

[tex]{\large{\boxed{\underline{\underline{\underline{\red{\bf Area\;of\;square\;=(side)^2}}}}}}} \bigstar[/tex]

[tex]\sf :\implies Area\;of\;door=(1)^2[/tex]

[tex]\sf :\implies Area=1\;m^2[/tex]

[tex]{\large{\boxed{\underline{\underline{\underline{\red{\bf Area\;of\;square=(side)^2}}}}}}} \bigstar[/tex]

[tex]\sf :\implies Area\;of\;1\;window=(0.5)^2[/tex]

[tex]\sf :\implies Area\;of\;1\;window=0.25\;m^2[/tex]

Now

[tex]\sf :\implies Area\;of\;2\;window=0.25\times2[/tex]

[tex]\sf :\implies Area\;of\;2\;window=0.5\;m^2[/tex]

Now

[tex]\sf :\implies Area\;to\;be\;painted=Ar.\;of\;4\;walls-(Ar.\;of\;1\;door+Ar.\;of\;2\;window)[/tex]

[tex]\sf :\implies Area\;to\;be\;painted=124-(1+0.5)[/tex]

[tex]\sf :\implies Area\;to\;be\;painted=124-1.5[/tex]

[tex]\sf :\implies Area\;to\;be\;painted=122.5\;m^2[/tex]

Now

We will simply multiply the area and rate

[tex]{\large{\boxed{\underline{\underline{\underline{\red{\bf Cost=Area \times Rate}}}}}}} \bigstar[/tex]

[tex]\sf :\implies Cost=122.5\times 2[/tex]

[tex]\sf :\implies Cost =Rs.245[/tex]

Therefore,

Cost of painting is Rs. 245