Question

John buys 20 m of fencing to create a dog pen. How much more area will the dog have if John builds a circular pen rather than a square one?

Answer 1

Given:

Length of fencing= 20m

To Find:

The difference in the area of circular and square pen=?

Step-by-step explanation:

For sqaure pen,

the perimeter of square pen will be

4(sides of square) = 20

side of square = 5m

now we can calculate the area of square pen,

area(A) = $side^{2}$ = 5 × 5 = 25m²

For the circular pen,

the perimeter of the circular pen will be

2π(radius) = 20

radius = $\frac{20}{2\times 3.14}$ = 3.18

now we can calculate the area of the circular pen,

area(B) = π(radius)² = 31.84 m²

Now, the difference between the two is

= B - A = 31.84 - 25 = 6.84

thus the dog will have 6.84m² more area if he builds the circular pen.