Answer :
To find the difference in the areas of the two square fields, we start by understanding the problem:
Initial Information:
- We have two square fields, let's call them Field A and Field B.
- The area of Field A is 1 hectare.
Conversion of Units:
- 1 hectare is equal to 10,000 square meters.
- Therefore, the area of Field A = 10,000 square meters.
Understanding the Broadened Field:
- Field B is broader by 1%, which means each side of Field B is 1% longer than a side of Field A.
Side Length Calculation:
- Let the side of Field A be [tex]s[/tex]. Since the area is 10,000 sq. meters, [tex]s^2 = 10,000[/tex].
- Therefore, [tex]s = \sqrt{10,000} = 100[/tex] meters.
- The side of Field B will be [tex]1\%[/tex] longer than Field A, thus:
[tex]\text{Side of Field B} = s \times 1.01 = 100 \times 1.01 = 101 \text{ meters}[/tex]
Area of Field B:
- Area of Field B [tex]= (101)^2 \text{ square meters}[/tex]
- [tex]101^2 = 101 \times 101 = 10,201 \text{ sq. meters}[/tex]
Difference in Areas:
- Difference [tex]= \text{Area of Field B} - \text{Area of Field A}[/tex]
- Difference [tex]= 10,201 - 10,000 = 201 \text{ square meters}[/tex]
Therefore, the difference in the areas is 201 square meters.
The correct answer is option B: 201 sq. metres.
