Question

Help!!!!!

The midpoints of the slides of a square are joined to its vertices as shown. What is the ratio of the area of the shaded square inside to the area of the original square

Answer 1

1/5

Explanation:

It is easy to see a right triangle on each side of the original square with its hypotenuse on the side of the original square, each with an area of 2⋅A2=A. Thus the total area of the original square is 5A, or the ratio of the area of the shaded square to the original square is 1/5.