I good to figure this out without doing using Pythagorean identities is to look at this is with a little bit of geometry. Key things to notice are the 5 cm side lengths. AB and ED are both 5 cm, and the dotted line indicates that point D is the midpoint between CE. If one side of the midpoint is 5 cm, that means the other side is, so CD is also 5 cm. This shows that ABCD is a perfect square. Now figuring out EF is a little trickier, but visually we can see that point A is 5 cm above the line CE, and also makes a right angle with points F and E. We're given angle values, and both of these are 45 degrees. This means that if you drew a straight line from A to the middle of EF, the two triangles created are symmetrical. If one of these sides we know is the same length as AD, then the other must be as well. So we get 2 x 5cm, or 10 cm.
https://cdn.discordapp.com/attachments/629152685584809984/652987283607257098/20191207_163729.jpg
A picture to explain cutting the triangle into two symmetrical ones.