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 other of its sides. Find the total area of the margin.

Answer 1

Hint: First we calculate the length and width of the cardboard after subtracting the length of margin from the given length and breadth. Then, as we know that the cardboard is rectangular in shape, we use the formula of the rectangle to calculate the area of the rectangle. Then, subtract the area of margin from it to get the required answer.

Complete step by step answer:
We have given that a picture is painted on cardboard 8 cm long and 5 cm wide. Also, there is a margin of $1.5\text{ cm}$ along each other of its sides.

We have to find the area of the margin.
As the cardboard is rectangular in shape, so the area of cardboard will be
$\text{Area=length }\!\!\times\!\!\text{ width}$
As given length $=8\text{ cm}$ and width $=5\text{ cm}$
So, we will get that the actual area will be
$\begin{align}
  & \text{Area=8}\times \text{5} \\
 & \text{Area}=40\text{ c}{{\text{m}}^{2}} \\
\end{align}$
Now, as we have given that there is a margin of $1.5\text{ cm}$ along each other of its sides, so the length and width of the cardboard will get reduced by $1.5+1.5=3\text{ cm}$.
So, the reduced length will be $8-3=5\text{ cm}$
Reduced width will be $5-3=2\text{ cm}$
So, the reduced area of the cardboard will be $5\times 2=10\text{ c}{{\text{m}}^{2}}$
Now, the area of margin will be $\text{actual area-reduced area}$
$\begin{align}
  & \Rightarrow 40-10 \\
 & =30\text{ c}{{\text{m}}^{2}} \\
\end{align}$
So, the total area of the margin is $30\text{ c}{{\text{m}}^{2}}$.

Note: In this question we have given the inner margin, so we reduce the actual length and width to get the required solution. If the outer margin were given in the question we have to add the value of margin to the length and width to get the correct answer.