8.3 Perimeter and Area 479 Circumference and Area of Circles A commonly used plane figure that is not a polygon is a circle. A circle is a set of points equidistant from a fixed point called the center. A radius, r, of a circle is a line segment from the center of the circle to any point on the circle (Fig. 8.33). A diameter, d, of a circle is a line segment through the center of a circle with both end points on the circle. Note that the diameter of the circle is twice its radius. The circumference, C, is the length of the simple closed curve that forms the circle. The formulas for the area and circumference of a circle are given in the following box. Learning Catalytics Keyword: Angel-SOM-8.3 (See Preface for additional details.) Example 2 Ladder on a Building During fire-safety training, a 13-foot ladder is placed against the wall of a building and the base of the ladder is 5 feet from the bottom of the wall (see Fig. 8.32). How high up the wall does the ladder reach? 5 ft ? 13 ft Figure 8.32 Solution The ground, the building wall, and the ladder form a right triangle. The ground and the building wall form the legs of the right triangle (sides a and b, respectively), and the ladder forms the hypotenuse (side c). By the Pythagorean theorem, a b c b b b b b (5) (13) 25 169 144 144 12 2 2 2 2 2 2 2 2 2 + = + = + = = = = Subtracted 25 from both sides of the equation. Take the square root of both sides of the equation Therefore, the ladder reaches 12 feet up the wall. 7 Now try Exercise 47 Circumference C = 2Sr Area A = Sr2 Radius Diameter Figure 8.33 Circumference and Area of a Circle r C r A r 2 2 π π = = The symbol pi, ,π was introduced in Chapter 5. Recall that π is approximately 3.14. However, when solving problems, you should use the π key on your calculator to get a more accurate answer.
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