Question

A circular field has perimeter 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 field.
16 In the adjoining figure.​

Answer 1

Answer: 22050 m² .

Step-by-step explanation:

Hey there !!

Let the radius of the circular field be r m .

Perimeter of the circular field = Circumference of the field .

=> 660 = 2πr .

\begin{gathered}\begin{lgathered}= > 660 = 2 \times \frac{22}{7} \times r. \\ \\ = > r = \frac{660 \times 7}{2 \times 22} . \\ \\ \therefore r = 105m .\end{lgathered}\end{gathered}

•°• 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 .