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.

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Answer 1

Given

The length of the cardboard $=8cm$

The breadth of the cardboard$=5cm$

Step 1- Area of Cardboard

Area of the cardboard = length × breadth

$$\begin{gathered} =8\times 5 \\ =40{cm}^2 \end{gathered}$$

Step 2- Area of cardboard when margins are not included

From the figure,

The new length of the cardboard when the margin is not included $=(8-1.5-1.5)cm=5cm$

The new breadth of the cardboard when the margin is not included $=(5-1.5-1.5)cm=2cm$

The new area of the cardboard $=$new length $\times$new breadth

$$\begin{gathered} =5\times 2 \\ =10{cm}^2 \end{gathered}$$

Step 3 - Area of the margin

The area of margin$=$ Area of the cardboard $-$Area of the cardboard when the margin is not included

$$\begin{gathered} =(40-10)c{m}^2 \\ =30{cm}^2 \end{gathered}$$

Hence, the total area of the margin is $30{cm}^2$