the square inside the circle has sides of 20cm long.
-
The diagonal of the square is also the diameter of the circle, so you have to find the length of the diagonal and then use C = πD to find the circumference.
Since the diagonal of a square makes the hypotenuse of a 45-45-90 triangle, you can use the Pythagorean theorem to find its length. Let s = the length of one side of the square and d = its diagonal.
s² + s² = d²
2s² = d²
And since we know the length of the side is 20 cm...
2(20 cm)² = d²
2(400 cm²) = d²
800 cm² = d²
d = √(800 cm²) = 28.3 cm
Which is also the diameter of the circle, so...
C = π√(800 cm²) = π(28.3 cm) = 88.9 cm
I hope that helps. Good luck!
Since the diagonal of a square makes the hypotenuse of a 45-45-90 triangle, you can use the Pythagorean theorem to find its length. Let s = the length of one side of the square and d = its diagonal.
s² + s² = d²
2s² = d²
And since we know the length of the side is 20 cm...
2(20 cm)² = d²
2(400 cm²) = d²
800 cm² = d²
d = √(800 cm²) = 28.3 cm
Which is also the diameter of the circle, so...
C = π√(800 cm²) = π(28.3 cm) = 88.9 cm
I hope that helps. Good luck!
-
If the sides of the square are 20 cm long, then its diagonal is
sqrt(20^2 + 20^2)
= sqrt(400 + 400)
= sqrt(800)
= 20sqrt(2)
This is the diameter of the circle.
The radius is therefore 10sqrt(2).
The area is therefore 200 pi cm^2
sqrt(20^2 + 20^2)
= sqrt(400 + 400)
= sqrt(800)
= 20sqrt(2)
This is the diameter of the circle.
The radius is therefore 10sqrt(2).
The area is therefore 200 pi cm^2
-
find the middle of the square then measure that point to the edge of the circle which you times by two to give you the length of the straight line through the circle and the circumference is double that.