Area of a Square Inside a Circle Example 3įind the area of the shaded parts of the circle that are outside square below. To find the area of the square we need to work out 2r 2, where r=6 in. In this case, the diameter of the circle is known, which is equal to twice the value of the radius. Area of a Square Inside a Circle Example 2 To find the area of the square we need to work out 2r 2, where r=4cm. We can also say that the perimeter of the square is 4 x √2 r = 4√2 r Square Inside a Circle Area ExamplesĪrea of a Square Inside a Circle Example 1 So the Area of the Square Inside the Circle is 2r 2 The area of the square can now simply be found by multiplying two adjacent sides together to give: Pythagoras' theorem states that the sum of the squares of the two smaller sides of the triangle is equal to the square of the hypotenuse (which in this case is equal to 2r).Īs s is the vaue for the side of the square, this gives us:
Let's look closely at the right triangle that has been made by the diagonal of the square:Īs the triangle is a right triangle, we can use Pythagoras' theorem to find the missing side s. You can also see that the diagonal and two sides of the square into two right triangles. This means that the length of the diagonal is 2r, where r is the radius of the circle. You will notice that the diagonal of the square is also the diameter of the circle as the diagonal goes from one side of the circle to the other through the center. Let's start by looking at the four corners of the square and draw in one of the diagonals. For those of you who like to know how things work, and why the formula is 2r 2, we will show you how it can be found below!