Question

A picture is painted on cardboard $8cm$long and$5cm$wide such that there is a margin of$1.5cm$along each of its sides. Find the total area of the margin.

Answer 1

Hint: Use formula of area of rectangle i.e, $l * b$, where $l$ is length and $b$ is breadth of rectangle.

Given:
Length$\left( l \right)$ and width$\left( b \right)$ of cardboard$ = 8cm$and $5cm$respectively.
And length of margin along each other of its sides$ = 1.5cm$
Therefore area of cardboard including margin$ = l \times b$
                                                                                   $ = 8 \times 5 = 40c{m^2}$
Now excluding margin
Length$ = 8 - 1.5 = 6.5cm$
Width$ = 5 - 1.5 = 3.5cm$
Therefore area of cardboard excluding margin$ = l \times b$
                                                                                    $ = 6.5 \times 3.5 = 22.75c{m^2}$
Therefore area of margin = area of cardboard including margin - area of cardboard excluding margin
                                           $ = 40 - 22.75 = 17.25c{m^2}$
Hence area of margin is $17.25c{m^2}$

Note: - In such types of questions first calculate the total area including margin then area excluding margin then subtract these two areas we will get the required area of margin.