Question

In the adjoining figure, find the area of the path (shown shaded) which is 2 m all around​

Answer 1

Answer:

316cm sq

Step-by-step explanation:

length of outer rectangle =100m

breadth of outer rectangle =60m

difference between outer rectangle and inner rectangle lengths or breadths = 2m

length of inner rectangle = 100–2 = 98

breadth of inner rectangle = 60–2 = 58

[rectangle area = l× b]

outer rectangle = 100 × 60 = 6000

inner rectangle = 98 × 58 =5684

{shaded region area = area of outer rectangle – area of inner rectangle}

= 6000–5684

= 316 cm sq

Answer 2

Given:

◕A rectangle has the length 100m and the breadth 60m

◕ A path 2m is made all around.

To Find:

 ✦The area of the path made in the rectangle.?

Solution:

➳ Now, we have got the measurements of the rectangle and the measurements of the path, so, it's said to find the area of the path.

➵ As the path divides the rectangle into 2 rectangles so, let's consider the area of the outer rectangle as area¹ and the area of the inner rectangle as area²

${\longrightarrow}\blue{ \underline{ \boxed{ \pink{ \mathfrak{ area \: of \: the \: path \: = \: area \: of \: \: rectangle_1 -\: rectangle_2}} }} \bigstar}$

Now let's find the area of the outer rectangle:

$\sf \: \dashrightarrow \orange{area \: of \: a \: rectangle = l \times \: b } \:$

⇴ let's substitute the values and find its area

$\longrightarrow { \sf{ \: area \: of \: the \: rectangle = lenght \ \: breadth}} \\ \\ \\ \: \longrightarrow \sf \: area \: of \: the \: rectangle = 100 \times 60 \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \sf \: area \: of \: the \: rectangle = 6000 {m}^{2} \bigstar \: \: \: \: \: \: \: \: \: \:$

❶hence, the area of rectangle¹ is 6000m²

→ Now, let's find the area of the inner rectangle:

◕ As a path of 2 m is made around so, the measurements of the inner rectangle will be:

$\longmapsto \rm \: length = 100 -( 2 +2) m \\ \\ \longmapsto \rm \: length = 96m \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longmapsto \rm \: breadth = 60 - (2 + 2)m \\ \\ \longmapsto \rm \: breadth = 56m \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

❖ As we know that :

$\sf \: \dashrightarrow \orange{area \: of \: a \: rectangle = l \times \: b } \:$

❍ let's substitute the values now and find the area:

$\longrightarrow \sf \: area \: of \: the \: rectangle \: = lenght\times breadth \\ \\ \\ \longrightarrow \sf \: area \: of \: the \: rectangle \: = 56m \times 96m \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\\longrightarrow \sf \: area \: of \: the \: rectangle \: = 5376 {m}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

❷ hence , the area of the inner rectangle is 5376m²

◉ Now ,let's find the area of the path

$\longrightarrow \sf \: area \: of \: the \: path = area_{2} - area_{1} \: \: \: \\ \\ \\ \longrightarrow \sf \: area \: of \: the \: path = 6000 - 5376 {m}^{2} \\ \\ \\ \orange{ \longrightarrow \bf \: area \: of \: the \: path = 624 {m}^{2} \bigstar } \: \: \: \: \:$

∴ Area of the path equals 624m²

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More to know:

• Area of Square = Side x Side
• Area of Rectangle = Length × Breadth
• Area of Triangle = ½ × base x height
• Area of parallelogram = base x height
• Area of circle = πr²
• Area of Rhombus = ½ × product of its diagonals
• Area of Trapezium = ½ × height × sum of parallel sides
• Area of Polygon = sum of the area of all regions into which it is divided

hope this helps.!