Question

A painting 40 cm long and 28 cm wide is painted on a cardboard such that there is a margin 2 cm along each of its sides.Find the total area of the margin.​

Answer 1

• The total area of the margin = 256 cm².

Given :–

• The length of the painting = 40 cm long.
• The width of the painting = 28 cm wide.
• A margin is 2 cm along each if it's sides.

To Find :–

• The total area of the margin.

How to solve ?

We have to find the total area of the margin.

First, we need to find the total area of the painting with margin by the given values of the length of the painting and the breadth of the painting. Then, we need to find the length and the breadth of the painting without margin by the given values of the length and the breadth of the painting after getting the value of the length and the breadth of the painting without margin then we need to find the total area of the painting without margin. After getting the total area of the painting without margin we have to find the total area of the margin by subtracting the area of the painting with margin and the area of the painting without margin.

Solution :–

First, we need to find the total area of the painting with margin.

Total length with margin is 40 cm.

Total breadth with margin is 28 cm.

The area of the painting with margin = length × breadth

→ 40 cm × 28 cm

→ 1120 cm²

Now, we need to find the length and the width of the painting without margin.

According to the question,

A margin is 2 cm along each if it's sides.

So,

Length of the painting without margin = 40 cm – (2 cm + 2 cm)

→ 40 cm – 4 cm

→ 36 cm

Breadth of the painting without margin = 28 cm – (2 cm + 2 cm)

→ 28 cm – 4 cm

→ 24 cm

Now, we need to find the area of the painting without margin.

Area of the painting without margin = length × breadth

→ 36 cm × 24 cm

→ 864 cm²

Now, we have to find the total area of the margin.

Area of the margin = Area of the painting with margin – Area of the painting without margin

Now we have,

• Area of the painting with margin = 1120 cm².
• Area of the painting without margin = 864 cm².

→ 1120 cm² – 864 cm²

→ 256 cm²

Hence,

The total area of the margin is 256 cm².