A square of side length s is inscribed in a circle. Write the area of the circle as a function of s.
A. A=(pi*s^2)/2 B. A=pi*s^2 C. A=(pi*s)/square root of 2 D. A=(1/2)*s^2
I would have loved to be able to figure this out on my own, but I can't seem to do it. It would be awesome if someone could explain to me how I would solve this. Thank you!
A. A=(pi*s^2)/2 B. A=pi*s^2 C. A=(pi*s)/square root of 2 D. A=(1/2)*s^2
I would have loved to be able to figure this out on my own, but I can't seem to do it. It would be awesome if someone could explain to me how I would solve this. Thank you!
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The diagonal of the square is a diameter of the circle. By Pythagoras' theorem this is s sqrt2.
Hence the radius is s sqrt2/2 and so the area is pi s^2 /2, so the answer is A.Hope thats ok.
Hence the radius is s sqrt2/2 and so the area is pi s^2 /2, so the answer is A.Hope thats ok.
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Not sure how much help you need.
Draw a picture and visualize.
The diameter of the circle is the same as the diagonal of the square.
We know(?) the diagonal is √2* the side
so diag = dia = √2s
We know the area is = pi*dia^2/4
but dia = √2s
so A = pi*dia^2/4 = pi*(√2s)^2/4 = pi2s^2/4 = pi(s^2)/2
Draw a picture and visualize.
The diameter of the circle is the same as the diagonal of the square.
We know(?) the diagonal is √2* the side
so diag = dia = √2s
We know the area is = pi*dia^2/4
but dia = √2s
so A = pi*dia^2/4 = pi*(√2s)^2/4 = pi2s^2/4 = pi(s^2)/2
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From the length of the side you can work out the diagonal, which is equal to the diameter of the circle. From the diameter you can work out the area.