Question

The area of car parking, lawn, swimming pool and park is the same. Find the area of the remaining portion.

Answer 1

Hint: We will first calculate the area of the rectangle ADIO and then subtract the area of the other four regions from the total area of the ADIO. The area of the rectangle ADIO is the product of its length and its breadth. Also, the area of the other four regions will be the same as they have the same dimensions.

Complete step-by-step answer:
We are given that the area of car parking, lawn, swimming pool and park is the same.
We have to find the area of the remaining portion.
From the diagram we will subtract the four areas, the car-parking area, lawn area, park area and pool area from the total area.

Required area is \[{\text{area of }}ADIO - {\text{area of}}\left( {{\text{ }}ABPN + CDEF + GHIJ + KLMO} \right)\]
Now, \[ADIO\] is a rectangle with length as 50m and breadth as $30m + 10m + 30m = 70m$
Also, the area of the rectangle is the product of the length and breadth.
Then, area of \[ADIO\] is $70 \times 50 = 3500{m^2}$
Next, the area of the other 4 rectangles will be the same as they all have length as 20m and breadth as 30m.
That is, $20 \times 30 = 600{m^2}$
Then, the required area is
$
  3500 - \left( {600 + 600 + 600 + 600} \right) \\
  3500 - \left( {2400} \right) \\
   = 1100{m^2} \\
$
Hence, the area of the required area is $1100{m^2}$
Note: We can alternatively calculate the required area by adding the areas of KJGI, GHEF, BCFP, NPLM and PFGL, where area of the rectangle is the product of its length and breadth.