Points p and Q

Question

Hello

Please help me with this problem I don't understand it at all

Please add the steps to how you got the answer

Thank you!!!

 

Points P and Q are midpoints of two sides of the square. What fraction of the interior of the square is shaded? 

 

 

Answer 1

Without the figure, I'm making the following assumptions:

1. Points P and Q are on adjacent sides, not opposite sides
2. The "shaded area" is the square made by connecting point P to the center of the original square, then connecting the center to point Q

 

Let's call the length of each side of the original square a.  The original square would have an area of a·a = a².  Since points P and Q are midpoints, the shaded square would have sides = 1/2 of the sides of the original square, or a/2.  The area of the shaded region would be (a/2)·(a/2) = a²/4.  Hence it has 1/4 of the area of the original square.