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THE "NEW STUDENT'S REFERENCE  WORK

2211

5. To find the area of a regular polygon of more than four sides, divide the polygon into triangles, and the area of the polygon will be the sum of the areas of the triangles.

A circle is a plane figure bounded by a curved line, every point of which is equally distant from the center.

The circumference of a circle is its bounding line.

The diameter is a straight line drawn through the center and terminating in the circumference.

The radius is a straight line drawn from the center to the circumference. It is one-half of the diameter.

If the circumference of a circle is divided by its diameter, the quotient, expressed to the nearest ten-thousandth, is 3.1416. For ordinary use 3^ may be used in place of 3.1416.

Learn. 1. To find the circumference of a circle multiply the diameter by 3.1416 or 3f

2. To find the diameter of a circle, divide the circumference by 3.1416 or 3i

Circumference

Diameter Greek letter '* (pi).

3.1416.   This ratio is usually expressed by the

The area of the accompanying regular polygon (octagon) is the sum of the areas of the triangles. The area of a triangle equals \ the product of its base by its altitude.

The sum of the bases of the triangle = the perimeter of the polygon.

The altitude (0 N) of one of the triangles is the apothem of the polygon.

The area of this regular polygon = | of the perimeter X the apothem.

Eeproduce the above regular polygon, and using the same center, draw the circumference of a circle.

Notice.—The circumference of the circle and the perimeter of the polygon are very nearly the same. Also, the apothem of the polygon and the radius of the circle are very nearly the same.

If the number of sides of the polygon were increased, the perimeter of the polygon would almost coincide with the circumference of the circle, and the apothem and radius would be the same.