Question

A rectangular park is \[45{\text{ m}}\] long and \[{\text{30 m}}\] wide. A path \[{\text{2}}{\text{.5 m}}\] wide is constructed outside the park. Find the area of the park.

Answer 1

Hint: To calculate the answer to the above question, we have to find the area of the path. To find this area, we will first calculate the area of the park and after that we have to calculate the area of the park with a path. After subtracting these two values, we will get the desired answer for our question.

Formula used:
In order to find the answer to the above question, we will use the following three formulas:
\[{\text{Area of park = length}} \times {\text{breadth}}\] .
\[{\text{Area of park with path}} = {\text{ Length of park + 2}}\left( {{\text{breadth of path}}} \right){\text{ }} \times {\text{ Breadth of park + 2(breadth of path)}}\]
\[{\text{Area of path = Area of park with path}} - {\text{ Area of rectangular park}}\] .

Complete step by step solution:
We are required to find the area of the path.
To calculate the answer, we will first find the area of the rectangular park by using the 1) formula:
\[{\text{Area of park = length}} \times {\text{breadth}}\]
\[{\text{ = 45}} \times {\text{30}}\]
\[{\text{ = 1350c}}{{\text{m}}^2}\] .
Now, we have to calculate the area of park with path, we will use the 2) formula:
\[{\text{Area of park with path}} = {\text{ Length of park + 2}}\left( {{\text{breadth of path}}} \right){\text{ }} \times {\text{ Breadth of park + 2(breadth of path)}}\]
\[
   = 45 + 2.5 + 2.5 \times 30 + 2.5 + 2.5 \\
   = 1750{\text{c}}{{\text{m}}^2} \\
 \]
After calculating the area of the park and the area of the park with the path, we can find the final answer.
Therefore, we will now use the 3) formula:
\[{\text{Area of path = Area of park with path}} - {\text{ Area of rectangular park}}\]
\[
   = 1750 - 1350 \\
   = 400{\text{c}}{{\text{m}}^2} \\
 \]
Hence, the correct answer for the above question Area of path \[ = 400{\text{c}}{{\text{m}}^2}\] .

Note: While solving such questions, you have to remember the formulas. In the above question we have used three simple formulas. The first formula was to calculate the area of a rectangle (park) and the other two formulas depended upon the question asked. Carefully, study the question and the diagram given along to derive the answer.