Question

A picture is painted on cardboard $8$ cm long and $5$ 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, first we have to find the total area of the cardboard. Then we find an area of painting. Both we find, to use the formula and doing some calculation. Finally we will subtract the area of the painting from the total area of the cardboard to find the area of the margin. Finally we get the required answer.

Formula used: \[{\text{Area of rectangle}} = {\text{length}} \times {\text{breadth}}\]

Complete step-by-step solution:
In this question stated as the given that the length of the picture painted on the cardboard is $8$ cm,
The width or the breadth of the picture painted on the cardboard is $5$ cm.
Apart from this, there is also a margin of $1.5$ cm which is there from all the sides surrounding the painting therefore, the painting and the cardboard can be visualized by the following diagram.

Now the total area of the cardboard is the length of the cardboard multiplied by the breadth of the cardboard, therefore the area is:
${{area = length \times breadth}}$
On substituting the value of length and breadth we get:
$\Rightarrow$${{area = 8 \times 5 cm}}$
On multiplication we get:
$\Rightarrow$${\text{area = 40c}}{{\text{m}}^{\text{2}}}$
Therefore, the total area of the cardboard is $40c{m^2}$
Now to calculate the area of the margin we have to first calculate the area of the painting
To calculate the area of the painting we have to first find out the length and breadth of the painting.
Since there is a margin of $1.5cm$ on all sides of the painting, therefore the margin has to be subtracted from the painting therefore,
The length of the painting is:
${\text{length = 8cm - 1}}{\text{.5cm - 1}}{\text{.5cm}}$
On simplifying we get:
$\Rightarrow$${\text{length = 5cm}}$
And the breath of the painting is:
$\Rightarrow$${\text{breadth = 5cm - 1}}{\text{.5cm - 1}}{\text{.5cm}}$
On simplifying we get:
$\Rightarrow$${\text{breadth = 2cm}}$
Now since we know the length and breadth of the painting, we will calculate the area of the painting, the area of the painting is:
$\Rightarrow$${\text{Area of painting}} = 5cm \times 2cm$
On simplifying we get:
$\Rightarrow$${\text{Area of painting}} = 10cm$
Now area of the margin is the area of the cardboard which is not the part of the painting, mathematically it could be written as:
$\Rightarrow$${\text{Area of margin = area of cardboard - area of painting}}$
On substituting the values, we get:
$\Rightarrow$${\text{Area of margin = 40c}}{{\text{m}}^{\text{2}}}{\text{ - 10c}}{{\text{m}}^{\text{2}}}$
On simplifying we get:
$\Rightarrow$${\text{Area of margin = 30c}}{{\text{m}}^{\text{2}}}$

Hence the area of margin is ${\text{30c}}{{\text{m}}^{\text{2}}}$

Note: The margin of a painting is the part of the cardboard which has no painting on it. A margin always surrounds the painting.
There is no direct formula to calculate the area of the margin of a painting.
The area of a rectangle formula should be remembered by a student to calculate the answer to these types of questions.