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.
Please Answer with proper calculation​
sorry it is subject math

Answer 1

Given:-

• Length of rectangular paper = 14 cm
• Breadth of rectangular paper = 12 cm
• Perimeter of square = 24 cm

To Find:-

• Area of piece of paper left.

Solution:-

Let us first find the area of the rectangle.

We know,

• Area of rectangle = Length × Breadth

Hence,

Area of paper = 14 × 12

Area = 168 cm²

∴ Area of the paper is 168 cm².

Now,

As it is given that perimeter of the square is 24 cm

We know,

• Perimeter of the square = 4 × side

Hence,

Perimeter = 24

=> 4 × side = 24

=> side = 24/4

=> side = 6 cm

∴ The side of the square is 6 cm.

Also,

We know,

• Area of square = (side)²

Hence,

Area of square = (6)²

=> Area of square = 36 cm².

Now,

Area of remaining piece of paper is as follows:-

• Area of rectangle - Area of square

Hence,

Area of remaining portion = 168 - 36

=> Area = 132 cm²

∴ Area of the remaining piece of paper is 132 cm²

______________________________________

Answer 2

Answer:

Question :-

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

Answer :-

• The area of the remaining piece of paper is 132cm².

Given :-

• Length of rectangular paper = 14cm.
• Breadth of rectangular paper = 12cm.
• Perimeter of square = 24cm.

To find :-

• We have to find the area of the remaining piece of paper.

Step-by-step explanation :-

• As we are given the length and breadth of rectangular paper.
• Then firstly, we will find out the area of the rectangular paper.
• So, by using the required formula we will find out the area of the rectangular paper.

We know that :-

${\underline{\boxed{\sf {Area\ of\ rectangle\ =\ length \times breadth}}}}$

Here,

• Length = 14cm.
• Breadth = 12cm.

By applying the values, we get :-

$\sf \mapsto {Area\ of\ paper\ =\ length \times breadth}$

$\sf \mapsto {Area\ of\ paper\ =\ 14 \times 12}$

$\therefore {\underline{\boxed{\tt {Area\ of\ paper\ =\ 168cm^2.}}}}$

• As we are given that the perimeter of the square is 24cm.
• So, by using the required formula we will find out the side of the square.

We know that :-

${\underline{\boxed{\sf {Perimeter\ of\ square\ =\ 4 \times side}}}}$

Here,

• Perimeter of the square is 24cm.

By applying the values, we get :-

$\sf \mapsto {Perimeter\ of\ square\ =\ 4 \times side}$

$\sf \mapsto {4 \times side\ =\ 24}$

$\sf \mapsto {side\ =\ \cancel \dfrac{24}{4}}$

$\therefore {\underline{\boxed{\tt {Side\ of\ square\ =\ 6cm.}}}}$

• Now, we have the side of the square. So now, we will find out the area of square.
• So, by using the required formula we will find out the area of square.

We know that :-

${\underline{\boxed{\sf {Area\ of\ square\ =\ (side)^2}}}}$

Here,

• Side of the square is 6cm.

By applying the values, we get :-

$\sf \mapsto {Area\ of\ square\ =\ (side)^2}$

$\sf \mapsto {Area\ of\ square\ =\ (6)^2}$

$\therefore {\underline{\boxed{\tt {Area\ of\ square\ =\ 36cm^2.}}}}$

• Now we have the area of both square and rectangle. So by subtracting the area of both square and rectangle, we will get the area of the remaining piece of paper.

$\sf \mapsto {Area\ of\ rectangle\ -\ Area\ of\ square}$

$\sf \mapsto {168\ -\ 36}$

${\therefore{\underline{\boxed{\tt {Area\ of\ remaining\ piece\ of\ paper\ =\ 132cm^2.}}}}}$