Answer
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Hint:
Find out the area of 4 walls and the ceiling individually. Add them together to get the total area. Then find out the costing for white wash.
Complete step-by-step answer:
Let $ABCD$ is the floor of a room. The length is $AB=CD=5m$ , breadth is $BC=CD=4m$ .
Height is 3m.
Now we have to find out the area of 4 walls.
Let us first find out the area of the wall which is perpendicular to the side $AB$.
For this wall the length is 5 meter, and the breadth is the height which is 3 meter.
We know that the area of a rectangle is = $length\times breadth$
So, the area of the wall which is perpendicular to the side $AB$ is:
$\begin{align}
&=\left( 5\times 3 \right){{m}^{2}} \\
&=15{{m}^{2}} \\
\end{align}$
The area of the wall which is perpendicular to the side $CD$ is basically the same as the area of the wall which is perpendicular to the side$AB$ . The length and the breadth, which is basically the height, are the same for both the walls.
Now the area of the wall which is perpendicular to the side $BC$ is:
$=\left( 4\times 3 \right){{m}^{2}}$
As the length of this wall is 4 meter and the breadth is 3 meter, which is the height.
So, the area is $=(4\times 3)=12{{m}^{2}}$
Similarly, the area of the wall which is perpendicular to the side $AD$ is basically the same as the area of the wall which is perpendicular to the side $BC$ . The length and the breadth, which is basically the height, are the same for both the walls.
Now, the total area of 4 walls is:
$=\left( 2\times 15 \right)+\left( 2\times 12 \right)=30+24=54{{m}^{2}}$
The area of the ceiling is the same as the floor.
So, the area of the ceiling is:
$=\left( 5\times 4 \right){{m}^{2}}=20{{m}^{2}}$
The total area is for white washing = total area of 4 walls + area of ceiling.
$\begin{align}
&=\left( 54+20 \right){{m}^{2}} \\
&=74{{m}^{2}} \\
\end{align}$
Now, the cost of white washing for one square meter is Rs. 7.50
The cost of white washing for 74 square meters is Rs.
$\begin{align}
&=74\times 7.50 \\
&=555 \\
\end{align}$
Therefore we need Rs. 555 to white wash the walls of the room and the ceiling.
Note: Alternatively we can directly use the area of four walls:
$=2\times \left( l+b \right)\times h$ , where $l$ is the length, $b$ is the breadth, $h$ is the height.
If we put the values in this formula:
$\begin{align}
& =2\times (5+4)\times 3=2\times 9\times 3 \\
& =54{{m}^{2}} \\
\end{align}$
So, the area of four walls is 54 square meters.
Find out the area of 4 walls and the ceiling individually. Add them together to get the total area. Then find out the costing for white wash.
Complete step-by-step answer:
Let $ABCD$ is the floor of a room. The length is $AB=CD=5m$ , breadth is $BC=CD=4m$ .
Height is 3m.
Now we have to find out the area of 4 walls.
Let us first find out the area of the wall which is perpendicular to the side $AB$.
For this wall the length is 5 meter, and the breadth is the height which is 3 meter.
We know that the area of a rectangle is = $length\times breadth$
So, the area of the wall which is perpendicular to the side $AB$ is:
$\begin{align}
&=\left( 5\times 3 \right){{m}^{2}} \\
&=15{{m}^{2}} \\
\end{align}$
The area of the wall which is perpendicular to the side $CD$ is basically the same as the area of the wall which is perpendicular to the side$AB$ . The length and the breadth, which is basically the height, are the same for both the walls.
Now the area of the wall which is perpendicular to the side $BC$ is:
$=\left( 4\times 3 \right){{m}^{2}}$
As the length of this wall is 4 meter and the breadth is 3 meter, which is the height.
So, the area is $=(4\times 3)=12{{m}^{2}}$
Similarly, the area of the wall which is perpendicular to the side $AD$ is basically the same as the area of the wall which is perpendicular to the side $BC$ . The length and the breadth, which is basically the height, are the same for both the walls.
Now, the total area of 4 walls is:
$=\left( 2\times 15 \right)+\left( 2\times 12 \right)=30+24=54{{m}^{2}}$
The area of the ceiling is the same as the floor.
So, the area of the ceiling is:
$=\left( 5\times 4 \right){{m}^{2}}=20{{m}^{2}}$
The total area is for white washing = total area of 4 walls + area of ceiling.
$\begin{align}
&=\left( 54+20 \right){{m}^{2}} \\
&=74{{m}^{2}} \\
\end{align}$
Now, the cost of white washing for one square meter is Rs. 7.50
The cost of white washing for 74 square meters is Rs.
$\begin{align}
&=74\times 7.50 \\
&=555 \\
\end{align}$
Therefore we need Rs. 555 to white wash the walls of the room and the ceiling.
Note: Alternatively we can directly use the area of four walls:
$=2\times \left( l+b \right)\times h$ , where $l$ is the length, $b$ is the breadth, $h$ is the height.
If we put the values in this formula:
$\begin{align}
& =2\times (5+4)\times 3=2\times 9\times 3 \\
& =54{{m}^{2}} \\
\end{align}$
So, the area of four walls is 54 square meters.
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