Question

Heyaa mate....❤
Please provide the solution of :- A circular field has a perimeter of 660 m.A plot in the shape of a square having its vertices on the circumference is marked in the field,Calculate the area of the square plot...

Answer 1

Circumference of the circular field = 660 m
2Πr = 660
=> r = 660/2Π
=(660/2)×(7/22)
= 4620/44
= 105 m

r = 105 m

Let side of square be a m

For the square to touch the boundary ,
Diameter of circle = Diameter of square

(where Diameter of square = 2r = 210)

a² + a² = (210)²
2a² = 210×210
=> a² = 22050 m

Answer 2

Hey there !!


Let the radius of the circular field be r m .

Perimeter of the circular field = Circumference of the field .

=> 660 = 2πr .

$= > 660 = 2 \times \frac{22}{7} \times r. \\ \\ = > r = \frac{660 \times 7}{2 \times 22} . \\ \\ \therefore r = 105m .$


•°• Diameter of the circular field = 2 × 105 = 210 m.

Vertices of the square plot lie on the circumference of the circle .

•°• Diameter of the circular field = Diagonal of the square plot .

=> 210 = BD .

In right ∆ABD,

AB² + AD² = BD² .

=> AB² + AB² = (210)² .

=> 2AB² = 210 × 210 .

=> AB² = ( 210 × 210 )/2 .

•°• AB² = 22050 m² .

•°• side² = 22050 m² .


✔✔ Hence, area of the square plot is 22050 m² ✅✅ .


THANKS



#BeBrainly.