Geometry: An Interactive Journey to Mastery

Solution
Imagine that the circle is drawn on a tiling of the plane
with squares, as shown in Figure 28.2.
Here, the rectangle has width 2, height 4, and, therefore,
area 8 units.
By the Pythagorean theorem, the side length of the square is 10 ,
so the square has area 10 units.
The area of the rectangle is indeed^45 the area of the square.
Study Tip
x This lesson is purely optional, and this topic does not appear in typical geometry courses. There are
no recommended study tips for this lesson other than to enjoy the lesson and let the thinking about it
strengthen your understanding of geometry as a whole.
Pitfall
x Don’t forget to have fun in your thinking of mathematics. This is a fun topic.

1. A square is inscribed in a circle, as is a rectangle with one side three times as long as the other. What can
   you say about the areas of these two quadrilaterals?


2. Twelve congruent equilateral triangles are used to construct a tetrahedron and an octahedron. The two
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Figure 28.2

Problems