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" Prove that the area of an inscribed regular hexagon is a mean proportional between the areas of the inscribed and the circumscribed equilateral triangles. "
Plane Geometry - Page 243
by Edward Rutledge Robbins - 1906 - 254 pages
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...are proportional to their apothems, their radii, or their sides. Proved with cor. 1. EXERCISES. 470. The area of an inscribed regular hexagon is a mean...proportional between the areas of the inscribed and circumscribed equilateral triangles. 471. Show how, with compasses alone, to divide a circumference...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...are proportional to their apothems, their radii, or their sides. Proved with cor. 1. EXERCISES. 470. The area of an inscribed regular hexagon is a mean...proportional between the areas of the inscribed and circumscribed equilateral triangles. 471. Show how, with compasses alone, to divide a circumference...
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Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 392 pages
...equilateral triangle is to the radius of the circumscribing circle as 3 is to 2. 614. The area of the regular hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles. 615. The square of a side of an inscribed equilateral triangle...
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Exercises in Wentworth's Geometry: With Solutions

George Albert Wentworth - Geometry - 1896 - 296 pages
...radius = Jú The apothem of the inscribed hexagon — J-RVS (Ex. 380). But TEACHERS EDITION. Ex. 392. The area of an inscribed regular hexagon is a mean...proportional between the areas of the inscribed and circumscribed equilateral triangles. PROOF. Area of inscribed equilateral A whose sido is a = |xf R...
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Plane Geometry

George D. Pettee - Geometry, Plane - 1896 - 272 pages
...circle, whose diameter is a chord of the outer circle, tangent to the inner circle. 396. The area of a regular hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles. MAXIMA AND MINIMA 289. Definitions. Of magnitudes of the same...
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Numerical Problems in Plane Geometry with Metric and Logarithmic Tables

Joe Garner Estill - Geometry - 1896 - 168 pages
...5. Prove that the area of any regular polygon of an even number of sides (2 n) inscribed in 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 or limits do these...
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Numerical Problems in Plane Geometry: With Metric and Logarithmic Tables

Joe Garner Estill - 1896 - 186 pages
...5. Prove that the area of any regular polygon of an even number of sides (2 n) inscribed in 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 or limits do these...
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Plane and Solid Geometry

James Howard Gore - Geometry - 1899 - 266 pages
...pentagon is 6 and a side is 4 ; find the perimeter and area of a regular pentagon whose apothem is 8. 4. The area of an inscribed regular hexagon is a mean...inscribed and the circumscribed equilateral triangles. 5. The area of an inscribed regular octagon is equal to that of a rectangle whose sides are equal to...
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New Plane Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 272 pages
...AO draw an arc cutting the circumference in C, D; draw CD, DB, BC, and prove A BCD equilateral. 444. The area of an inscribed regular hexagon is a mean...proportional between the areas of the inscribed and circumscribed equilateral triangles. 445. Show how, with compasses alone, to divide a circumference...
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The Elements of Plane Geometry

Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...inscribed equilateral triangle is equal to one half the area of the inscribed regular hexagon. Ex. 659. The area of an inscribed regular hexagon is a mean...proportional between the areas of the inscribed and circumscribed equilateral triangles. Proposition 217. Theorem. 254. The area of a circle is equal to...
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