Question

A picture is painted on a 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

Step-by-step explanation:

$\frak Given = \begin{cases} &\sf{Length\ of\ painted\ cardboard\ =\ 8cm.} \\ &\sf{Breadth\ of\ painted\ cardboard\ =\ 5cm.} \end{cases}$

To find:- We have to find the total area of the margin ?

☯️ Since, there is a margin of 1.5cm long from each of its side.

__________________

$\sf \therefore {\underline{Reduced\ length:-}}$

$\sf : \implies {8\ -\ (1.5\ +\ 1.5)\ =\ 8\ -\ 3\ =\ 5cm.}$

$\sf \therefore {\underline{Reduced\ breadth:-}}$

$\sf : \implies {5\ -\ (1.5\ +\ 1.5)\ =\ 5\ -\ 3\ =\ 2cm.}$

__________________

$\frak{\underline{\underline{\dag According\ to\ the\ question:-}}}$

$\sf \therefore {Area\ of\ margin\ =\ Area\ of\ cardboard\ (ABCD)\ -\ Area\ of\ cardboard\ (EFGH)}$

$\sf : \implies {(AB\ ×\ AD)\ -\ (EF\ ×\ EH)} \\ \\ \sf : \implies {(8\ ×\ 5)\ -\ (5\ ×\ 2)} \\ \\ \sf : \implies {40\ -\ 10} \\ \\ \sf : \implies {\purple{\underline{\boxed{\bf 30cm²}}}}\bigstar$

Hence:-

$\sf \therefore {\underline{The\ total\ area\ of\ margin\ is\ 30cm².}}$

Answer 2

$\frak Given = \begin{cases} &\sf{Length\ of\ painted\ cardboard\ =\ 8cm.} \\ &\sf{Breadth\ of\ painted\ cardboard\ =\ 5cm.} \end{cases}$

To find:- We have to find the total area of the margin ?

☯️ Since, there is a margin of 1.5cm long from each of its side.

__________________

$\sf \therefore {\underline{Reduced\ length:-}}$

$\sf : \implies {8\ -\ (1.5\ +\ 1.5)\ =\ 8\ -\ 3\ =\ 5cm.}$

$\sf \therefore {\underline{Reduced\ breadth:-}}$

$\sf : \implies {5\ -\ (1.5\ +\ 1.5)\ =\ 5\ -\ 3\ =\ 2cm.}$

__________________

$\frak{\underline{\underline{\dag According\ to\ the\ question:-}}}$

$\sf \therefore {Area\ of\ margin\ =\ Area\ of\ cardboard\ (ABCD)\ -\ Area\ of\ cardboard\ (EFGH)}$

$\sf : \implies {(AB\ ×\ AD)\ -\ (EF\ ×\ EH)} \\ \\ \sf : \implies {(8\ ×\ 5)\ -\ (5\ ×\ 2)} \\ \\ \sf : \implies {40\ -\ 10} \\ \\ \sf : \implies {\purple{\underline{\boxed{\bf 30cm²}}}}\bigstar$

Hence:-

$\sf \therefore {\underline{The\ total\ area\ of\ margin\ is\ 30cm².}}$