a square park of a side 100m. A road 5m wide is made all around the garden inside it. Find the area of the road.
Answers
Given,
The side of the square park is 100m
The road is 5m
To find,
The area of the road
Solution,
We know that the area of the square is calculated with the formula which is given below:
Area of square = Side x Side
Applying the formula to calculate the area of the square park
The area of square park = 100m x 100m
The area of square park = 10000 m^2
Now, the side of the square park other than the road = Side of the square park – Sides of the road at both the ends
Putting the values from above
We will get, The side of the square park other than road = 100m – (2 x 5m)
= 100m – 10m
= 90m
Then,
The area of the square park other than the road = 90m x 90m
= 8100m^2
Now, the area of the road = Area of the square park – Area of the square park other than the road
Putting the values from above
The area of the road = 10000m^2 – 8100m^2
The area of road = 1900m^2
Hence, the area of the road is 1900m^2
The area of road is 1900 m².
A square park of a side 100m. A road 5m wide is made all around the garden inside it.
We have to find the area of road.
- see diagram attached in the answer, shaded region shows the road made all round the garden inside it.
- It is clear that area of road is the difference of area of bigger square to smaller square.
∴ the area of road = area of bigger square - area of smaller square.
= (100 m)² - (90 m)²
using Algebraic formula, a² - b² = (a - b)(a + b)
= (100 - 90)(100 + 90) m²
= 10 × 190 m²
= 1900 m²
Therefore the area of road is 1900 m².
