The diagonal of a square can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the diagonal (d) of the square can be found as follows:
d^2 = 10^2 + 10^2
d^2 = 100 + 100
d^2 = 200
d = sqrt(200)
d = 10 x sqrt(2) cm
The diameter of the circle is equal to the diagonal of the square, so the diameter of the circle is also 10 x sqrt(2) cm.
The radius of the circle (r) is half the diameter, so:
r = (10 x sqrt(2))/2 cm
r = 5 x sqrt(2) cm
The area of the circle can be found using the formula:
A = pi x r^2
Substituting the values for r and pi:
A = 3.14 x (5 x sqrt(2))^2 cm^2
A = 3.14 x 50 cm^2
A = 157 cm^2
Therefore, the area of the circle is 157 sq cm (to two decimal places).
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Step-by-step explanation:
The diagonal of a square can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the diagonal (d) of the square can be found as follows:
d^2 = 10^2 + 10^2
d^2 = 100 + 100
d^2 = 200
d = sqrt(200)
d = 10 x sqrt(2) cm
The diameter of the circle is equal to the diagonal of the square, so the diameter of the circle is also 10 x sqrt(2) cm.
The radius of the circle (r) is half the diameter, so:
r = (10 x sqrt(2))/2 cm
r = 5 x sqrt(2) cm
The area of the circle can be found using the formula:
A = pi x r^2
Substituting the values for r and pi:
A = 3.14 x (5 x sqrt(2))^2 cm^2
A = 3.14 x 50 cm^2
A = 157 cm^2
Therefore, the area of the circle is 157 sq cm (to two decimal places).