Answer: 192 square centimeters
Explanation: In this problem, we will be using the Pythagorean Theorem: C^2=A^2+B^2 and the formula for the area of a Parallelogram: Area=Base*Height(h).
The base of the parallelogram is the longer side at the bottom which is 16cm. We have to find the height somehow. Hmmm. We notice that there is a triangle made up of dotted lines on the right side of the diagram. We can use the Pythagorean Theorem ONLY when we are given a Right Triangle. We know we have a right triangle because there is a right angle in it indicated by the square at the bottom-right of the diagram. The theorem states that C^2=A^2+B^2. The variable C represents the length of the longest side of the triangle and A and B represent the lengths of the other two sides. The longest side will always be opposite the right angle. This means that C is 13 cm or the longest side and 5 cm is one of the other sides. Plugging into the theorem we get, 13^2=5^2+A^2. A is the third side of the triangle or h which is our height. Solving for h we get 12 meaning our height is 12.
We can now finally plug back into Area=Base*height to get Area=16cm*12cm. Solving this we get that the Area is 192 cm^2.
Hope this helps!