Question

A rectangular field of 150m by 100m has a 10m path around it . find the area of the path
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Answer 1

Answer:

\underline\bold{\huge{Solution!!}}

Area of rectangular field

= l×b

= 150×100

= 15000 square. meter

Length of rectangle with path

= 150 + 10 + 10

= 170 m

Breadth of rectangular field with path

= 100 + 10 + 10

= 120 m

Area of rectangular field with path

= l × b

= 170 × 120

= 20400 square metres

Area of path = Area of Field with path - Area of field

= 20400 - 15000

= 5400 sq.metre

Answer 2

Given :

• Length of rectangular field = 150 m
• Breadth of rectangular field = 100 m
• Also, the rectangular field is covered with = 10 m

To Find :

• Area of the path.

Calculation :

✰ Here, we are given with the length (150 m) and breadth (100 m) of a rectangular field. Also, the field is enclosed by 10 m. So, in order to calculate the area of rectangle. Firstly, we have to find the measure of area of rectangular field.

First of all, let us calculate the length and breadth of a field.

$\red{\dag}$ Length of rectangular path :

$\longrightarrow \tt 150 + 10 + 10$

$\longrightarrow \bf 170 \: m$

$\red{\dag}$ Breadth of rectangular path :

$\longrightarrow \tt 100 + 10 + 10$

$\longrightarrow \bf 120 \: m$

Now, calculating the area of small rectangle field :-

$\pink{\dag}$ Area of small rectangular field :

$\longrightarrow \tt l \times b$

$\longrightarrow \tt 150 \times 100$

$\longrightarrow{\underline{\boxed{\tt{15000 \: m^2}}}}$

Therefore, the area of rectangular field is 15000 m².

$\pink{\dag}$ Area of big rectangular field :

Now, let us calculate the area of big rectangular field :-

We know that,

• Area of rectangle = length × breadth

Here,

• Length = 170 m
• Breadth = 120 m

Plugging the values,

$\longrightarrow \tt l \times b$

$\longrightarrow \tt 170 \times 120$

$\longrightarrow{\underline{\boxed{\tt{20400 \: m^2}}}}$

$\dag \: \underline{ \underline{ \boldsymbol{According \: to \: the \: Question : }}}$

Let us calculate the area of the path.

Concept :

• Area of rectangular path = Area of big field - Area of small field

Here,

• Area of big field = 20400 m²
• Area of small field = 15000 m²

Putting the values in the equation,

$\longrightarrow \tt 20400 \times 15000$

$\longrightarrow{\underline{\boxed{\pink{\pmb{\tt{5400 \: m^2}}}}}}$⠀

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$\therefore \underline{ \sf{Area \: of \: rectangular \: path \: is \: \bf{5040 \: m^2}}}$