Question

Scenery is painted on cardboard \[19\;cm\] long and $ 14\;cm $ wide, such that there is a margin of $ 1.5\;cm $ along each of its sides. Find the total area of the margin.

Answer 1

Hint: In this question, we need to determine the total area of the margin. Here the length and breadth of the painting is given. Since the painting is in the form of a rectangle we will use the area of the rectangle to determine the area of the painting with margin. Then subtract the value of margin from length and breadth to determine the area of the painting without margin. And, by subtracting both the areas we will get the total area of margin.

Complete step-by-step answer:
It is given that the total length of the painting is \[19\;cm\].
And, the total breadth of the painting is $ 14\;cm $ .
Also, there is a margin of $ 1.5\;cm $ along each of its sides.
Here, we need to determine the total area of the margin.
The scenery is in the shape of a rectangle.
Therefore, we know that the area of the triangle= $ length \times breadth $
Hence, the area of the painting including the margin= $ 19 \times 14 $
Therefore, the area of painting including margin= $ 266\,sq\,\;cm $
Now, let us determine the area of the painting without the margin.
Length of the painting without margin $ = 19 - \left( {1.5 + 1.5} \right) $
 $ = 19 - 3 $
 $ = 16\;cm $
Then, width of the painting without the margin= $ 14 - \left( {1.5 + 1.5} \right) $
 $ = 14 - 3 $
 $ = 11\;cm $
Therefore, area of the painting without the margin $ = 16 \times 11 $
Hence, area of the painting without the margin $ = 176\,sq\,\;cm $
Now, total area of the margin= total area of the painting with margin – total area of the painting without margin
 $ = 266 - 176 $
 $ = 90\,sq\,\;cm $
Hence, the total area of the margin is $ 90\,sq\,\;cm $ .
So, the correct answer is “$ 90\,sq\,\;cm $”.

Note: It is important to note here that the area of the rectangle= $ length \times breadth $ . We can use this method for similar questions, as it is the easiest method. Be careful while multiplying the length and breadth.