Question

A picture is painted on a cardboard 10 cm
long and 8 cm wide such that there is
a margin of 1.5 cm along each of its
side. Find the total area of the margin.​

Answer 1

Given -

• Length of cardboard = 10cm

• Breadth of cardboard = 8cm

• Width of margin = 1.5cm

To find -

• Total area of margin

Formula used -

• Area of rectangle = L × B

Solution -

In the question, we are given with the length and breadth of the cardboard and the width of the margin,and we need to find the total area of the margin. For that first we will find the area of the cardboard, then we will find the area of cardboard, including margin, after that, we will deduct the area of cardboard from the area of cardboard including margin. Let's do it!

According to question -

Length of cardboard = 10 cm

Breadth of cardboard = 8 cm

Area of cardboard = L × B

On substituting the values -

$\sf \longrightarrow \: area \: = l \: \times \: b \: \\ \\ \\ \sf \longrightarrow \: area \: = 10 \: cm \: \times \: 8 \: cm \: \\ \\ \\ \sf \longrightarrow \: area \: = 80 \: {cm}^{2}$

Now -

We will find the area of the cardboard including the margin, so the length of breadth with be increased, and we will add 1.5 two times in the length and breadth. Let's do it!

New length = 10 cm + (1.5 cm + 1.5 cm)

New length = 13 cm

New breadth = 8 cm + (1.5 cm + 1.5 cm)

New breadth = 11 cm

Now -

We have obtained the new length and breadth, now we will find the area of cardboard including margin.

Area of cardboard (including margin) = L × B

On substituting the values -

$\sf \longrightarrow \: area \: = l \: \times \: b \\ \\ \\ \sf \longrightarrow \: area \: = 13 \: cm \: \times \: 11 \: cm \\ \\ \\ \sf \longrightarrow \: area \: = 143 \: {cm}^{2}$

Now -

We have obtained both the areas, now we will reduce the area of cardboard including margin from the area of cardboard, that will give us the area of the margin.

Area of margin = Area of cardboard (including margin) - Area of cardboard.

$\sf \longrightarrow \: area \: = 143 \: cm \: - \: 80 \: cm \: \\ \\ \\ \sf \longrightarrow \: area \: = 63 \: {cm}^{2}$

$\therefore$ Total area of margin is 63cm²

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