Question

10. A rectangular piece of paper has a length of 14 cm and a breadth of 12 cm. A square piece
of paper of perimeter 24 cm is cut off from it. Find the area of the piece of paper left.​

Answer 1

Answer:

Given:

▪︎Length of rectangular piece of paper = 14cm

▪︎Breadth of rectangular piece of paper = 12cm

▪︎Perimeter of square cut through rectangular piece of paper = 24cm

To Find:

▪︎Side of square paper

▪︎Area of the piece of paper left

Solution:

➡️Area of Whole rectangular piece of paper

= length × breadth

= 14 × 12

= 168cm²

➡️Sides of a Square

= Perimeter ÷ 4

= 24 ÷ 4

= 6cm

➡️Area of square piece of paper

= Side × Side

= 4 ×4

= 16cm²

➡️Area of Paper left

= Area of whole paper - area of square piece

= 168 - 16

= 152cm²

Formula to be remembered:

▪︎Area of rectangle = length × breadth

▪︎Perimeter of rectangle = 2(length + breadth)

▪︎Area of square = Side²

▪︎Perimeter of square = 4 × side

Answer 2

Given :

• length of the rectangular piece of paper is 14cm
• breadth of the rectangular piece of paper is 12cm
• perimeter of a square piece cutted from it is 24cm

To find :

• the area of the piece of paper left

Solution

As we know,

Area of rectangle = $\boxed{\tt{length × breadth}}$

→ 14cm × 12cm

→ 168cm²

As we know,

Perimeter of square = $\boxed{\tt{4 × side}}$

→ 24cm = 4 × side

→ side = $\cancel \frac{24cm}{4}$

→ side = 6cm

Therefore,

As we know,

Area of square = $\boxed{\tt{side × side}}$

→ 6cm × 6cm

→ 36cm²

Now we have to find the area of the piece of paper left

• total area of the paper - area of the paper cutted

→ 168cm² - 36cm²

→ 132cm²

Hence, the area of the piece of the paper cutted is 132cm².