What is the area of a square inside a circle where the radius of the circle is 10centimetres?

Answer 1

314.16 cm2

This is not what I get... I get 200cm^2 and here is my reasoning:

The diameter of the circle is the same as the diagonal of the square so...

2r = diagonal of the square

Diagonal of the square is the hypotenuse of two triangles that form the square.

In a right triangle, a^2 +b^2=c^2 where c is the hypotenuse (diagonal of the square)

We can then write... 2r = c

we know that r= 10 so...

2(10)= c therefore c=20

back to pythagorean theorum... a^2+b^2=20^2

since it is a square, both sides are equal so b^2 must = a^2 or a^2+b^2= a^2+a^2 or (b^2+b^2)

so we can write a^2 + a^2 = 20^2

2a^2= 400 ----- therefore a^2= 200

Then, a = square root of 200 but we would multiply a times itself anyway (side x side = area) so the correct answer would be 200 cm^2.