Video: KS2-M19 • Paper 2 • Question 17

These two shapes have the same perimeter. The length of each side of the hexagon is 8 cm. Calculate the area of the square.

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Video Transcript

These two shapes have the same perimeter: a regular hexagon and a square. The length of each side of the hexagon is eight centimetres. Calculate the area of the square.

We know these two shapes have the same perimeter. The perimeter of a 2D shape is the distance all the way around. We find the perimeter by adding together the sum of all the sides. We’re told that the length of each side of the hexagon is eight centimetres. And we know that a hexagon has six sides. So we could either add together six lots of eight or multiply six by eight. Six times eight is 48. So the perimeter of the hexagon is 48.

This means that the square also has a perimeter of 48 centimetres. But a square only has four sides. So we can calculate the length of one side by dividing the perimeter by four. 48 divided by four is 12. Now we know the length of the sides of the square. Each side is 12 centimetres.

Now we know the length of the sides, we can calculate the area of the square. We find the area of a square by multiplying the length times the width. So the area of the square is 12 centimetres multiplied by 12 centimetres. 12 12s are 144. And we write area as centimetres squared. The area of the square is 144 centimetres squared.

First, we calculated the perimeter of the hexagon by multiplying eight by six. We knew this meant the perimeter of the square was also 48 centimetres. And we divided this by four to tell us the length of one of the square sides. Once we knew the length of the square sides, we were able to calculate the area by multiplying 12 by 12, to give us our answer 144 centimetres squared.