Question

A square park has each side of 100 m. At each corner of the park, there is a flowerbed in the form of a quadrant of radius 14 m as shown in the figure. Find the area of the remaining part of the park.

Answer 1

Given: A square park with side 100 m. At each corner there is a flowerbed that is a quadrant of radius 14 m.

Step-wise calculation:

1. Area of the square

= Side²

= 100²

= 10,000 m²

2. Area of one quadrant (radius r = 14 m)

= `1/4 xx π xx r^2` 

= `1/4 xx π xx 14^2` 

= 49π m²

3. Total area of four quadrants

= 4 × 49π

= 196π m²

4. Area of remaining part

= Area of square – Area of flowerbeds

= 10,000 – 196π m²

5. Numeric approximation:

196π = 196 × 3.14159265

= 615.75216

So, remaining area

= 10,000 – 615.75216 

= 9,384.24784 m²

Exact area = 10,000 – 196π m²

Approximate area = 9,384.25 m² to two decimal places.