Books Books
The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Mensuration of lines, surfaces, and volumes - Page 98
by David Munn - 1873

Plane and Solid Geometry

Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...another hexagon. Compare the areas of the two hexagons. 23. The area of an inscribed regular hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles. 24. Join the alternate vertices of any regular polygon and show that a similar polygon is thus formed....

Plane [and Spherical] Trigonometry for Colleges and Secondary Schools

Daniel Alexander Murray - Plane trigonometry - 1908 - 358 pages
...the triangle is equal to the square of half the base. 15. (a) Show that the area of a regular polygon inscribed in a circle is a mean proportional between the areas of an inscribed and circumscribing polygon of half the number of sides. (6) The sides of a triangle are...

Plane Geometry Developed by the Syllabus Method

Eugene Randolph Smith - Geometry, Plane - 1909 - 424 pages
...equal to two sides and the included angle of the other. 587. The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles. 588. Three equal circles are described each tangent to the other two. If the common radius is R, find...

College Entrance Examination Papers in Plane Geometry

Geometry, Plane - 1911 - 192 pages
...without it. 6. Prove that the area of any regular polygon of an even number of sides (2ri) inscribed jn a circle is a mean proportional between the areas of the inscribed and the circumscribed polygons of half the number of sides. If n be indefinitely increased, what limit...

Elements of Plane Trigonometry

Daniel Alexander Murray - Plane trigonometry - 1911 - 158 pages
...""— . Write two similar formulas coS2" involving b, c. 9. (a) Show that the area of a regular polygon inscribed in a circle is a mean proportional between the areas of an inscribed and circumscribing polygon of half the number of Bides, (b) The sides of a triangle are...

Plane and Solid Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...area of a regular hexagon whose side is 6 inches. Ex. 1006. The area of an inscribed regular hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles. Ex. 1007. The figure represents a flower bed drawn to the scale of 1 inch to 20 feet. Find the number...

Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...pentagon divide each other in extreme and mean ratio. Ex. 1309. The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles. Ex. 1311. The diagonals drawn from a vertex of a regular decagon divide that angle into eight equal...

Schultze and Sevenoak's Plane Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...pentagon divide each other in extreme and mean ratio. Ex. 1309. The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles. Ex. 1311. The diagonals drawn from a vertex of a regular decagon divide that angle into eight equal...