Video: Finding the Perimeter of a Square given the Radius of an Inscribed Circle

In the following figure, find the perimeter of the square ๐ฟ๐‘€๐‘๐‘‚ given that the length of the circleโ€™s radius = 3 cm.

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Video Transcript

In the following figure, find the perimeter of the square ๐ฟ๐‘€๐‘๐‘‚ given that the length of the circleโ€™s radius is three centimetres.

To find the perimeter of the square, we need to find the distance all the way around its edge. Thatโ€™s the sum of its four side lengths. As this shape is a square, all of its side lengths are the same. So its perimeter is equal to four ๐ฟ, where ๐ฟ represents the side length of the square.

The only other piece of information weโ€™ve been given is that the radius of this circle, which has been inscribed inside the square, is three centimetres. The radius of a circle is the distance from the centre to any point on the circumference. So, for example, itโ€™s the length of this line here. Itโ€™s also the length of this line here, connecting the centre of the circle to the opposite side of the circumference.

The diameter of the circle is twice the radius. Thatโ€™s two lots of three centimetres, which is six centimetres. But as the circle is inscribed in the square, meaning that points on its circumference touch the square but donโ€™t go outside it, this means that the diameter of the circle is the same as the side length of the square. We can see that the side ๐‘๐‘‚ is six centimetres.

As ๐ฟ๐‘€๐‘๐‘‚ is a square, all of its sides are the same length, which means the vertical height of the square is also six centimetres. But we could also have seen this if we drawn on our radii vertically rather than horizontally. So the perimeter of this square can be found by multiplying its side length six by four. Four multiplied by six is 24. And the units for this perimeter will be centimetres because these are the units that weโ€™re given for the circleโ€™s radius.

Weโ€™ve found that the perimeter of the square ๐ฟ๐‘€๐‘๐‘‚ is 24 centimetres.

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