Path is nothing but the measure of boundaries of the shapes. The area of the path is defined as the region occupied by the shape inside or outside. Here we can apply the concept of Area of rectangle or area square to find the area of paths. This is the major concept in the basic theory of **Mensuration**. The students can learn the different techniques to find the area of the path of different shapes like rectangle, square, circle, etc.

## What is the Area of Path?

The area of the path is the subtraction of the area of the outer rectangle/square and the area of the inner rectangle/square. It is defined as the space left between the area of two 2-d figures or paths. This article helps to learn the theory of the area of the path in depth.

### Area of the Path Formula

Area of the path = area of outer rectangle – area of inner rectangle

Area of the path = area of outer square – area of inner square

### Solved Problems on Area of the Path

Here we use the concept of the area of rectangle and area of the square. Know how to calculate the area of the path with the help of the solved example problems.

**1. A rectangular plot is 20 cm long and 15 cm wide. The inner rectangular plot is 12 cm long and 10 cm wide. Draw the diagram of the rectangular plot and find the area of the path?**

Solution:

Given the length of the outer rectangle is 20 cm

Width of the outer rectangle is 15 cm

We know that,

Area of the rectangle = l × w

A = 20 cm × 15 cm

A = 300 sq. cm

Also given the length of the inner rectangle = 12 cm

Width of the inner rectangular plot = 10 cm

We know that,

Area of the rectangle = l × w

A = 12 cm × 10 cm

A = 120 sq. cm

Total Area of the path = 300 sq. cm – 120 sq. cm = 180 sq. cm

**2. A park is of length 30 m and 20 m wide. A path 1.5 m wide is constructed outside the rectangular garden. Find the area of the path?**

Solution:

Given the length of the inner rectangle = 30 meter

The wodth of the inner rectangle = 20 meter

We know that,

Area of the rectangle = l × w

A = 30 m × 20 m

A = 600 sq. meter

AB = 20 + 1.5 + 1.5 = 23 m

BC = 30 + 1.5 + 1.5 = 33 m

Area of the outer rectangle = l × w

A = 33 m × 23 m

A = 759 sq. meter

Area of the path = Area of outer rectangle – Area of inner rectangle

Therefore Area of the path = 759 sq. m – 600 sq. m

A = 159 square meters

Thus the area of the path of rectangular garden is 159 sq. meters.

**3. A path 10 m wide runs along inside the square park of side 1000 m. Find the area of the path? **

Solution:

Given that,

A path 10 m wide runs along inside the square park of side 1000 m.

PS = PQ = QR = RS = 1000m

Find the sides of the inner square.

Width = 10m

AB = 1000 – 10 – 10 = 980m

AB = BC = CD = AD = 980 m

We know that

Area of the square = side × side

A = 1000 × 1000 = 1,000,000 m²

Area of the inner square = s × s

A = 980 × 980 = 960,400 m²

Area of the path = 1,000,000 m² – 960,400 m²

= 39,600m²

Thus the area of the path is 39,600m²

**4. A rectangular box is 10 cm long and 8 cm wide. A path of the uniform width is 5 cm. Find the area of path?**

Solution:

Given,

A rectangular box is 10 cm long and 8 cm wide. A path of the uniform width is 5 cm

Find the length and width of the outer rectangle

AD = 10cm + 5cm + 5cm = 20cm

AB = 8cm + 5cm + 5cm = 18cm

Area of the outer rectangle = l × w

A = 20cm × 18cm

A = 360 sq. cm

Area of the inner rectangle = l × w

A = 10cm × 8cm

A = 80 sq. cm

Area of the path = Area of outer rectangle – Area of inner rectangle

A = 360 sq. cm – 80 sq. cm

A = 280 sq. cm

Thus the area of path is 280 sq. cm

**5. A 1m wide path runs outside and around a rectangular park of length 6m and width 4m. Find the area of the path?**

Solution:

Given,

A 1m wide path runs outside and around a rectangular park of length 6m and width 4m.

Area of inner rectangle = l × w

A = 6m × 4m

A = 24 sq. m

Area of outer rectangle = (6m + 1m + 1m) × (4m + 1m + 1m)

A = 8m × 6m

A = 48 sq. m

Area of the path = Area of the outer rectangle – Area of inner rectangle

A = 48 sq. m – 24 sq. m

A = 24 sq. meters

Thus the area of the path is 24 sq. meters.

### FAQs on Area of the Path

**1. How to find the area of the path?**

We can find the area of a path by subtracting the area of outer shapes and the area of inner shapes.

**2. What is the formula for Area of Path?**

Area of the path = Area of outer rectangle/square – Area of inner rectangle/square

**3. How to calculate the area of the path for square?**

You can calculate the Area of the path using the formula Area of Path = Area of outer square – Area of inner square