Question

A rectangular park is surrounded by a path which is 2.5 m wide. If the length and breadth of the
rectangular park are 20 m and 15 m respectively, find the area of the path.
​

Answer 1

Given :-

Width of the path = 2.5 m

Length of rectangular park = 20 m

Breadth of the rectangular park = 15 m

To Find :-

The area of the path.

Analysis :-

Find the area of the smaller rectangle.

Add the width of the path to the length and breadth and find the area of the bigger rectangle.

Subtract the area of smaller rectangle from the bigger rectangle to find the area of the path.

Solution :-

We know that,

• l = Length
• b = Breadth
• a = Area

Given that,

Length (l) = 20 m

Breadth (b) = 15 m

By the formula,

$\underline{\boxed{\sf Area \ of \ a \ rectangle=Length \times Breadth}}$

Substituting their values,

Area = $\sf 20 \times 15$

Area = 300 m²

Therefore, the area of the rectangle excluding the path is 300 m²

Now,

Area of the rectangle including the path = (Length + 2.5 m) × (Breadth + 2.5 m)

Substituting them,

Area = $\sf (20+2.5) \times (15+2.5)$

Area = $\sf 22.5 \times 17.5$

Area = 393.75 m²

Therefore, the area of the rectangle including the path is 393.75 m²

Finding the area of path,

Area of path = Area of bigger rectangle - Area of smaller rectangle

Substituting them,

Area of path = $\sf 393.75-300$

Area of path = $\sf 93.75 \ m^{2}$

Therefore, the area of path is 93.75 m²