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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

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 or class=

Respuesta :

Answer:

1/5

Step-by-step 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.