Illustration: The decagon and the rectangle can be composed of the same triangular insets.
In the material there are two decagon insets, one consisting of a whole decagon and the other of a decagon divided into ten triangles.
Here it is demonstrated that a rectangle equivalent to a decagon may have one side equal to the whole hypotenuse and the other equal to half of the perimeter.
The photograph shows the pieces of the insets--the decagon and the equivalent rectangle--and beneath each one there are the small equal triangles into which it can be subdivided.
Page 281 shows a table taken from our geometry portfolio, representing the equivalence of a decagon to a rectangle having one side equal to the perimeter and the other equal to half the hypotenuse.
Another inset shows the equivalence of the decagon and a rectangle which has one side equal to the perimeter of the decagon and the other equal to half of the altitude of each triangle composing the decagon.
If we make the sides of this triangle equal to the radius of the given circle, then the base will be the side of the regular decagon inscribed in the circle.
This side being known the decagon can be constructed, and if the vertices are joined alternately, leaving out half their number, we obtain the regular pentagon.
Below the arches are the chapels which surround the decagon in symmetrical fashion.
The great decagon of St. Gereon's is covered with a domed roof, also divided into ten sections by groins or ribs, which rise gracefully from the slender shafts at the angles, meeting at the apex in a boss.
The purpose of this problem is to prepare for the construction of the regular decagon and pentagon.
It follows from the 4th Book of Euclid, that the rectangle under the side of a regular decagoninscribed in a circle, and that side increased by the radius, is equal to the square of the radius.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "decagon" in a variety of sentences. We hope that you will now be able to make sentences using this word.
