A circle is inscribed in a square. The number of square units in the area and the number of units in the perimeter of the square are the same. What is the area of the circle in terms of pi?

Explain your thought process.

I completely don't understand this question. Can you help me? Thank you! :)

Your sentence "The number of square units in the area and the number of units in the perimeter of the square are the same " is not clear.

Is the number of square units in the area of the circle and the number of units in the perimeter of the square the same
or
Is the number of square units in the area of the square and the number of units in the perimeter of the square the same ??

Please clarify, the solutions will be different.

Of course! Let's break down the question step by step.

We are given that a circle is inscribed in a square. When a circle is inscribed in a square, it means that the circle's diameter is equal to the length of one side of the square.

Next, we are told that the area of the square is equal to the perimeter of the square. To find the area of a square, we square the length of one side, and to find the perimeter, we multiply the length of one side by 4.

Let's denote the side length of the square as "s". Therefore, the area of the square is s^2, and the perimeter of the square is 4s.

Given that the area and perimeter are equal, we can set up the equation:
s^2 = 4s

To solve for s, we can subtract 4s from both sides and set the equation equal to zero:
s^2 - 4s = 0

Factoring out an "s" from both terms, we get:
s(s - 4) = 0

This equation tells us that either s = 0 or (s - 4) = 0. Since the length of a side cannot be zero, we use the second equation to find s:
s - 4 = 0
s = 4

So, the side length of the square is 4.

Now we can find the diameter of the inscribed circle, which is equal to the side length of the square:
d = 4

To find the radius of the circle (which is half the diameter), we divide the diameter by 2:
r = d/2
r = 4/2
r = 2

Finally, we can find the area of the circle using the formula:
Area = π * r^2
Area = π * 2^2
Area = π * 4

Hence, the area of the circle in terms of π is 4π square units.