Question

Find the total area of four walls in each rectangular room having length $ 10m $ , breadth $ 5m $ , height $ 4m $ ?

Answer 1

Hint: In order to find the area of four walls, first list out the things that are given, for example, length, breadth and height. Then substitute all the values in the formula to find the area of four walls: Area of four walls $ = Perimeter\left( {floor} \right) \times height $ .

Complete step-by-step answer:
We are given a rectangular room whose length is $ 10m $ , breadth is $ 5m $ and the height is $ 4m $ .
The rough diagram for the room is:
           

From the formula to find the Area of four walls of a rectangular room, we know that:
Area of four walls $ = Perimeter\left( {floor} \right) \times height $ .
Since, we know that Perimeter of a rectangle is $ 2\left( {length + breadth} \right) $ .
Substituting this value, the Area of four walls is expanded as:
Area of four walls $ = 2\left( {length + breadth} \right) \times height $ .
Putting the value of length, breadth and height above and we get:
 $
  Area = 2\left( {length + breadth} \right) \times height \\
  Area = 2\left( {10 + 5} \right) \times 4 \;
  $
We would be solving the formed equation further, for that initiating with solving the brackets, to get:
\[
  Area = 2\left( {10 + 5} \right) \times 4 \\
  Area = 2\left( {15} \right) \times 4 \\
  Area = 2 \times 15 \times 4 \;
 \]
Simplifying, it further we get:
 $
  Area = 30 \times 4 \\
  Area = 120{m^2} \;
  $
Therefore, the total area of four walls in each rectangular room having length $ 10m $ , breadth $ 5m $ , height $ 4m $ is $ 120\;{m^2} $ .
So, the correct answer is “ $ 120\;{m^2} $ ”.

Note: A rectangular room, is in the form of a cuboid. Area of four walls is also called the Lateral Surface area of a cuboid. Lateral Surface area is the Area of a cuboid without bases.
If we need to calculate the total surface area of the rectangular room or cuboid then just add the area of the faces of bottom or top to the lateral surface area.