Question

In a square shaped park whose side measures 28m rectangular pond is located at the center with dimension 3m and 2m. The area of the park excluding the pond is
A 784sq.m
B 6sq.m
C 778sq.m
D 708sq.m

Answer 1

Hint: In this problem, a rectangular pond with dimensions 3m and 2m is located at the center of the square shaped park whose side measure is 28m. In this condition we have to find the excluding area between the square shaped park and the rectangle shaped pond. We can first find the area of the rectangle using the formula and we can find the area of the square, we can then subtract the area of the square from the area of the rectangle to get the required answer.

Complete step by step answer:
By using the area formula for both square and rectangle, where
Area of rectangle
\[\Rightarrow l\times b\] ……. (1)
Then the area of the square
\[\Rightarrow {{a}^{2}}\]
From the given dimensions of the rectangle,
\[\begin{align}
  & \Rightarrow l=3m \\
 & \Rightarrow b=2m \\
\end{align}\]
For the square all the four sides are equal, therefore from the given side measures
\[\Rightarrow a=28\]
By substituting the values in the area of the rectangle (1),
\[= 3\times 2\]
We get,
\[= 6m\]
Then substituting the area of the square
\[= {{28}^{2}}\]
We get,
\[= 784m\]
To find the area of the park which excluding the pond, we have to reduce the area of the square from the area of the rectangular pond, therefore
\[= 784-6\]
We get,
\[= 778sqm\]
Therefore the area of the pond excluding the park is 778sqm.

So, the correct answer is “Option C”.

Note: Students will make mistakes in finding the length and breadth of the rectangle. All the four sides of the square are always equal, this must be remembered. We must remember the formulae for the area of the rectangle and area of the square where area of the square is \[{{a}^{2}}\] and the area of the rectangle is \[l\times b\].