Exercises on mensuration

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W. & R. Chambers, 1874 - Measurement - 157 pages
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Page 134 - ... by equal regular polygons of either three, four, or six sides. 262. A plane surface may be entirely covered by a combination of squares and regular octagons having the same side, or by dodecagons and equilateral triangles having the same side.
Page 136 - From this it readily follows that all the three lines drawn from the angles of a triangle to the middle of the opposite sides, pass through one and the same point.
Page 137 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Page 108 - ... respectively, on a side and the volume of a prism of the same altitude whose base is a section of the frustum parallel to its bases and equidistant from them.
Page 68 - Find the area of a sector of a circle whose radius is 21 feet, the length of the arc being 15 feet.
Page 132 - Prove that the area of the regular hexagon inscribed in a circle is twice the area of the inscribed equilateral triangle. Verify this fact by cutting a regular hexagon out of paper, and folding it. Ex. 1195. The side of an equilateral triangle circumscribed about a circle is twice the side of an inscribed equilateral triangle.
Page 134 - A = the side of the similar circumscribed polygon, then, 2aR 2AR -a-) V(4R 3 +A 3 ) 272. If o = the side of a regular polygon inscribed in a circle whose radius is R,, and a...
Page 9 - Large School-room Maps of England, Scotland, Ireland, Europe, Palestine, Asia, Africa, and North and South America, unvarnished, each, 12s.
Page 114 - Find the radius of a sphere which has the same volume as a cone whose height = h, and radius of base 6.
Page 63 - Show that the areas of similar triangles are to each other as the squares of the homologous sides.

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