Question

What is the ratio of
area of outermost
square to that of the
shaded region, if
each of the marked
points are
the
midpoints of the line
segments they are
touching?

Answer 1

the ratio of the area of the square to that of the shaded portion is 2:1.

For example,

if one aide of the outermost square is 4 units. Since the midpoint divides the line segment into two equal parts. So, one side of the respective square will be in the 2 units and 2 units respectively. Then, the distance between two midpoints there is a vertex is 2 unite for each. With that, we get that the one side of the shaded portion is 2√2.

Now, if you find the area of the figures, you will get that the area of the outermost square is 16 units sq and that if the shades figure will be 8 units sq.

Hence, proved that the ratio of the area of the outermost square to that of the shaded figure is 2:1