Question

A circular plot has perimeter of 660 m. A plot in the shape of a square having its vertices on the circumference of the field is marked in the field. Calculate the area of the square field.

• A. 225 m²
• B. 244 m²
• C. 144 m²
• D. 110 m²

Answer 1

The correct option is

D

110 m²

Let r m be the radius of a circular plot.

Perimeter of the plot = $2\pi r$= 660 m

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

Diameter of the plot = AC = 2 $\times$ 105 = 210 m.

Let the side of the square be x m

In right angled triangle ABC,

$\Rightarrow$ $A{C}^2=A{B}^2+B{C}^2$

$\Rightarrow$$2x^2$ = $(210{)}^2$

$\Rightarrow$$x^2$ = $\frac{210}{2}\times 210$

$\therefore x^2=22050$

Area of square field = 22050 $m^2$