QUESTION:

Determine where the hole came from when the geometric shapes are re-arranged as in the lower layout.

Make a large scale drawing of the two layouts and calculate the following areas:

TOP LAYOUT:

The area of the four geometric shapes = 32.0 units

The area of the right triangle inclosing the four geometric shapes = 32.5 units

Therefore the slope of the line forming the top of the geometric shapes is an under slope when compared to the cord or hypotenuse of the right triangle, where the triangle area is bigger by 0.5 units.

BOTTOM LAYOUT:

The total area of the four geometric shapes plus the 1.0 unit hole = 33.0 units

Therefore the slope of the line forming the top of the geometric shapes is an over slope when compared to the cord or hypotenuse of the right triangle, where the area of the triangle is smaller by 0.5 units.

SUMMARY:

The 0.5 unit difference between the area of the triangle and the area of the geometric shapes in the top layout plus the 0.5 unit difference between the area of the geometric shapes and the area of the triangle in the lower layout = 1.0 unit = the 1.0 unit hole.

This quiz was included in the monthly quizzes because it shows that some times the answer to a problem is not obvious at first glance and a more detailed study is required to see the difference.

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