Question

A squarepark is of side
100 m . A path 5 m wide is made all around the garden inside it . Find the area of the path . ​

Answer 1

Given :-

• Side of the Square park = 100m
• Wide of the Path = 5m

To Find :-

• Area of the Path

Solution :-

★ Area of the Square Park ★

➞ Area of the Square park = (Side)²

➞ Area of the Square park = Side × Side

➞ Area of the Square park = 100 × 100

➞ Area of the Square park = 10000m²

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★ Side of the Garden ★

➞ Side of the Garden = 100 - 5 + 5

➞ Side of the Garden = 100 - 10

➞ Side of the Garden = 90m

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★ Side of the Garden ★

➞ Area of the Garden = (Side)²

➞ Area of the Garden = Side × Side

➞ Area of the Garden = 90 × 90

➞ Area of the Garden = 8100m²

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★ Area of the Path ★

➞ Area = Park's Area - Garden's Area

➞ Area = 10000 - 8100

➞ Area of the Path = 1900m²

________________

Therefore, Area of the Path = 1900m²

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Answer 2

Given:

• A square park has the side 100m

• A path of 5m wide is made inside the garden all around.

To Find:

• The area of the path

Solution:

◐ Now here, we have got the side of the square which is 100m and siad that there is a path made of 5m all around the square and we have to find the path.

Now,

↦ The area of path equals the area of the outer square - inner square.

★Let's find the area of outer square★

${ : \implies} \sf \: area \: of \: a \: square = {side}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \\ { : \implies} \sf \: area \: of \: the \: square = {100}^{2} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \\ { : \implies} \sf \: area \: of \:the\: square = 10000 {m}^{2} \bigstar$

❍ hence,

the area of the outer square equals 10000m²

★Now we find the value of the inner square★

As a path of 5 m is made so, the sides of the inner square are reduced by 5 m from both the sides of a side.

${ \longrightarrow }\sf \: side \: of \: the \: inner \: square = 100 - (5 - 5) \\ \\ \\\longrightarrow \: \sf \: side \: of \: the \: inner \: square = 100 -10 \: \: \: \: \: \: \\ \\ \\ \longrightarrow\sf \: side \: of \: the \: inner \: square = \orange{90m \bigstar} \: \: \: \: \: \: \: \: \: \: \: \:$

Now , as we found the side of the inner square let's substitute it and find the area

${ : \implies} \sf \: area \: of \: a \: square = {side}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \\ { : \implies} \sf \: area \: of \:the \: square = {90}^{2} \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \\ { : \implies} \sf \: area \: of \: the \: square = 8100 {m}^{2}$

❍ hence,

the area of the inner square equals 8100m²

↬Now let's find the area of the path

${ : \implies} \sf \: area \: of \: the \: path \: = 10000 - 8100 \\ \\ \\ \\ { : \implies} \sf \: area \: of \: the \: path \: = \pink{ \underline{ \boxed{1900 }\bigstar}} \: \: \: \: \: \: \: \: \: \:$

↦ therefore, the area of the path equals 1900m²

More to know:

• area of rectangle = length × breadth

• area of a triangle = ½bh

• area of a parallelogram = base × hieght

• area of a rhombus = d¹ × d²/2