On my paper, there's a circle drawn inside of a square, whose side length is 12. I have to find diameter, radius, area, area in terms of pi, ...
For the diameter first of all, would it be 12? Or do I have to subtract?
Thanks.
Yes. The diameter is 12.
So then, :
Would the radius be 6?
Would the area be 354.9456? or 113.04?
You're right about the radius = 6. And your second answer is correct for the area.
The area is PI * r^2.
3.14 * 36 = 113.04.
Thanks.
To find the diameter of the circle, you do not subtract anything from the square's side length. The diameter is simply the distance across the circle, passing through its center.
In this case, the square has a side length of 12. Since the circle is drawn inside the square, it will be inscribed within the square.
The diagonal of a square is always equal to the diameter of the circle that can be inscribed inside the square. So, to find the diameter, you need to find the length of the square's diagonal.
To calculate the diagonal of a square, you can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the diagonal of the square will serve as the hypotenuse of a right-angled triangle, with each side of the square serving as one of the other two sides. So, let's use the Pythagorean theorem:
a² + b² = c²
Since the sides of the square have the same length, we will call each side "a" and the diagonal "c". Plugging in the values, we have:
a² + a² = c²
2a² = c²
Next, substituting the side length of the square, we get:
2(12)² = c²
2(144) = c²
288 = c²
To find the value of c (the diagonal), we need to calculate the square root of 288:
c ≈ √288 ≈ 16.97 (rounded to two decimal places)
Therefore, the diameter of the circle inscribed inside the square is approximately 16.97 units.