2006-11-05 16:36:01 · 2 answers · asked by Sang 1 in Science & Mathematics ➔ Mathematics
15 inches
The side of a regular hexagon inscribed in a circle is the same as the radius of the circle. In fact, if you connect the center of the circle to each vertex of the hexagon (with a straight line segment), then you will have 6 equilateral triangles that all meet at the center of the circle.
2006-11-05 16:49:24 · answer #1 · answered by actuator 5 · 1⤊ 0⤋
Answer: 15 inches.
Details: A regular polygon of six sides - a regular hexagon - has each interior angle = 120 deg.
Draw the radii to the vertices of the hexagon, 6 triangles are
formed, which can be proved to be identical to each other: Consider two adjacent triangles, the three sides of one are equal to the corresponding sides of the other; hence congruent.
That makes the angles made by radii with the sides of the hexagon, at its vertices, all 60 deg.
Therefore all the 6 triangles are equilateral and that makes the hexagon's side = radius = 15 inches.
2006-11-06 01:02:11 · answer #2 · answered by Inquirer 2 · 0⤊ 0⤋