Question

A square has a side that measures 2.75 units. What is the area of a circle with a circumference that equals the perimeter of the square?

Answer 1

9.63 square units

Explanation:

It is given that, a square has a side that measures 2.75 units.

To find the perimeter of square

Perimeter = 4 * side

= 4 * 2.75

= 11 units

To find the radius of circle with circumference 11 units

Circumference = 2πr

2πr = 11

r = 11/2π

To find the area of circle

Area of circle = πr²

= π(11/2π)²

= (π * 11 * 11/4π²)

= 121/4π

= 121/(4 * 3.14)

= 9.63 square units

Answer 2

Answer: 9.62 square units

Explanation:

Given : The side of square = 2.75 units.

Then the perimeter of the square will be :-

Now, let the circumference of the circle be :_

`C=11`

Also, the circumference of circle is given by :-

`C=2\pi r\\\\\Rightarrpw\ 11=2\pi r\\\\\Rightarrow\ r=\frac1}{2\pi}=(11)/(2(3.14))\approx1.75`

Area of circle :

`A=\pi r^2\\\\\Rightarrow\ A=(3.14)(1.75)^2=9.61625\approx9.62\text{ square units}`