Question

A room \[12.5m\] long and \[10.5m\] wide is surrounded by a verandah \[2m\] wide all round it. Find the area occupied by the verandah.

Answer 1

Hint: We are asked to find the area occupied by verandah so here we will use the formula of area of rectangle for finding area of the room which is Area of rectangle = Length \[ \times \]Breadth. Then we find the area of the verandah surrounding the room and lastly we will calculate the area occupied by the verandah by subtracting the area of the room from the area surrounded by the verandah.

Formula used:
The formula that we will use in order to solve the above problem is
Area of rectangle = Length \[ \times \]Breadth

Complete step by step solution:
Here we are given length of the room \[(l)\]= \[12.5m\]
Breadth of the room \[(b)\]= \[10.5m\]
Therefore we will calculate the area of the room by the formula \[l \times b\]
\[ \Rightarrow 12.5 \times 10.5 \\
   \Rightarrow 131.25{m^2} \\ \]
So the length of the verandah will be
\[ \Rightarrow 12.5 + 2 + 2 \\
   \Rightarrow 12.5 + 4 \\
   \Rightarrow 16.5m \\ \]
Breadth of the verandah will be
\[
   \Rightarrow 10.5 + 2 + 2 \\
   \Rightarrow 10.5 + 4 \\
   \Rightarrow 14.5m \\
 \]
Area=\[l \times b\]
\[
   \Rightarrow 16.5 \times 14.5 \\
   \Rightarrow 239.25{m^2} \\
 \]
Now as we need to calculate the area of verandah
\[
   \Rightarrow 239.25 - 131.25 \\
   \Rightarrow 108{m^2} \\
 \]
So the area of the verandah will be \[108{m^2}\]

Note:
While solving the above problem we need to remember the basic standard formulas for areas that include the formula for finding the area of the rectangle. Keep in mind that the unit will be in square while calculating area so take care of the units while finding the area. At last we are asked to find the area occupied by the verandah so do not forget to subtract the area of room from the area surrounded by the verandah. Here the measurements given were in meters so we have used squared meters for area.