Question

Shivangi had a picture that is $40cm$ long and $28cm$ wide in the centre of the panel leaving a border of $1cm$ on all sides. Find the area of the panel and border by the picture.

Answer 1

Hint: Given us are the dimensions of the picture and the width of the border of the panel. We are to determine the whole length and breadth of the panel by adding the length of picture to twice the width of the borders of the panel, because the border extends on both sides of the picture, so we are to add twice the width of borders. Then we can calculate the area of the panel by using the formula,
$\text{Area} = \text{Length} \times \text{Breadth }$
Then, to find the area of the borders, we are to subtract the area of the panel from the area of the picture.

Complete step by step answer:
Given, length of picture, $l = 40cm$
Breadth of picture, $b = 28cm$
Width of borders of panel, $w = 1cm$

Therefore, length of panel, $L = l + 2w$
[Since, the width extends on both sides of the picture]
$ \Rightarrow L = \left( {40 + 2 \times 1} \right)cm$
$ \Rightarrow L = 42cm$
And, breadth of panel, $B = b + 2w$
[Since, the width extends on both sides of the picture]
$ \Rightarrow B = \left( {28 + 2 \times 1} \right)cm$
$ \Rightarrow B = 30cm$
Therefore, the area of the panel ABCD is, $A = L \times B$
$ \Rightarrow A = \left( {42 \times 30} \right)c{m^2}$
$ \Rightarrow A = 1260c{m^2}$
Therefore, area of panel ABCD is $1260c{m^2}$.
Now, area of border of panel $ = \left( {{\text{area of panel}}\,{\text{ABCD}}} \right){\text{-}}\left( {{\text{area of picture PQRS}}} \right)$
Therefore, area of border of panel, $a = A - {A_0}$
Where, ${A_0} = $ area of picture PQRS $ = l \times b$
So, $a = \left( {L \times B} \right) - \left( {l \times b} \right)$
Now, substituting the value of $l$ and $b$, we get,
$ \Rightarrow a = \left[ {1260 - \left( {40 \times 28} \right)} \right]c{m^2}$
Simplifying the calculations, we get,
$ \Rightarrow a = \left[ {1260 - 1120} \right]c{m^2}$
$ \Rightarrow a = 140c{m^2}$
Therefore, the area of the borders of the panel ABCD is $140c{m^2}$.

Note:
This problem can also be done in another way as, first by calculating the area of each rectangle formed in the border of the panel by the width of the panel and by each side of the picture, then, adding the area of the rectangles to the four squares formed at each corner of the border of the panel. This will give us the total area of the border of the panel. Then, we can calculate the area of the panel by adding the area of the picture to the border of the panel.