16. Jessica cuts four identical squares from the corners of a square sheet of paper as shown. The total area she cut off is 16 square centimeters and the area of the cross that remains is 9 square centimeters. What is the perimeter of the cross in centimeters? Pause if you want to try and solve it. Let me quickly draw a larger picture of this just so we have a more clear idea. So we have this sort of cut out on each side and we're left with a cross in the middle. So we know that the total area that she cut off is 16 square centimeters and there's four identical squares so each one of these is 4 square centimeters. A square with a total area of 4 has a side length of 2 because 2 times 2 equals 4. So each of these sides going from here to where we cut out on each side is 2. So this is also 2, so is this, and also on the bottom. But how long is this? Well the total area of the big square is 16 plus 9 which is 25. And a square that has an area of 25 has a side length of 5. So the total area of the big square is 5. And we know this is 2, we know this is 2, so the remaining part over here has to be 1 because 1 plus 2 plus 2 is 5. So each of these is 1, all of these over here are 1, these are all 2, and importantly these sides on the inside are also 2. So we can use that to now figure out the perimeter of this cross. We have 4 sides each of which have length 1 so that's going to be 4. And then we have 1, 2, 3, 4, 5, 6, 7, 8 sides each of which have length 2. So 8 times 2 is 16 and 4 plus 16 equals 20. So the total perimeter of this cross is going to be 20 which is option C.

geometry

square

perimeter

area

cross