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In the following figure, find the perimeter of the square ๐ฟ๐๐๐ given that the length of the circleโs radius is three centimetres.
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To find the perimeter of the square, we need to find the distance all the way around its edge.
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Thatโs the sum of its four side lengths.
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As this shape is a square, all of its side lengths are the same.
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So its perimeter is equal to four ๐ฟ, where ๐ฟ represents the side length of the square.
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The only other piece of information weโve been given is that the radius of this circle, which has been inscribed inside the square, is three centimetres.
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The radius of a circle is the distance from the centre to any point on the circumference.
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So, for example, itโs the length of this line here.
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Itโs also the length of this line here, connecting the centre of the circle to the opposite side of the circumference.
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The diameter of the circle is twice the radius.
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Thatโs two lots of three centimetres, which is six centimetres.
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But as the circle is inscribed in the square, meaning that points on its circumference touch the square but donโt go outside it, this means that the diameter of the circle is the same as the side length of the square.
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We can see that the side ๐๐ is six centimetres.
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As ๐ฟ๐๐๐ is a square, all of its sides are the same length, which means the vertical height of the square is also six centimetres.
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But we could also have seen this if we drawn on our radii vertically rather than horizontally.
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So the perimeter of this square can be found by multiplying its side length six by four.
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Four multiplied by six is 24.
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And the units for this perimeter will be centimetres because these are the units that weโre given for the circleโs radius.
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Weโve found that the perimeter of the square ๐ฟ๐๐๐ is 24 centimetres.