PRE-ALGEBRA

How do you find the area of a circle? Proof: If you cut a circle into tiny wedges (slices), you could arrange the wedges into a shape that a parallelogram as shown in the picture below. Area: Circles (10-3) This suggests that the area of a circle is similar to the area of a parallelogram, where the radius (distance from the center to a point on the circle), r, is like the height, h, of the parallelogram, and the base (bottom) of the parallelogram is about half of the circumference (distance around), C, of the circle (the other half is the top). A = bh Use the formula of the area of a parallelogram. A = (½C) · rSubstitute ½C for b and r for h. A = ½(2pr) · rSince the formula for circumference, C, is 2  r, substitute 2  r for C. A = 1 · 2 ·  r · rSimplify. 2 1 A =  r · r=  r 2 A circle =  r 2 The area of circle is the product of  and the square of the radius. A circle =  r 2

PRE-ALGEBRA Find the exact area of a circle with diameter 20 in. A = r 2 = (10) 2 Substitute r = d = = 100Simplify. Since is an irrational number that never ends, the exact area is 100 in. 2. Area: Circles LESSON 10-3 Additional Examples

PRE-ALGEBRA How do you estimate the area of a circle? Area: Circles (10-3) To estimate the area of a circle, change  (pi) into its decimal form, which is approximately Example: Estimate the area of a circle with a diameter of 5 miles. A =  r 2 Use the formula of the area of a circle. =  (2.5) 2 Since r = ½d = ½(5) = 2.5, substitute 2.5 for r. =   6.25 exact area  3.14 · 6.25 Use 3.14 for p.  approximate area  20 rounded to nearest whole The area is about 20 square miles.

PRE-ALGEBRA A TV station’s weather radar can detect precipitation in a circular region having a diameter of 100 mi. Find the approximate area of the region. A = r 2 The area of the region is about 7,850 mi 2. = (50) 2 r = d = = 2,500exact area (2,500)(3.14)Use 3.14 for . = 7,850approximate area Area: Circles LESSON 10-3 Additional Examples

PRE-ALGEBRA How do you find the area of an irregular figure that has part of a circle in it? Example: Estimate the area of the lawn. Area: Circles (10-3) To find the area of an irregular figure, separate it into figures (like circles and parallelograms) that you know how to find the areas of. If one of the figures is part of a circle, multiply that fraction of a circle by ½  r 2. (   3.14). Area of region that is half of a circle A circle = ½  r 2 Area of half of a circle (  r 2 is area of entire circle) = ½  (15) 2 Since r = ½d = ½(30) = 15, substitute 15 for r. = ½  (225) Simplify. =   112.5exact area  3.14  Use 3.14 for p.  approximate area  353 rounded to nearest whole Area of region that is a rectangle. A rectangle = bh Area of a rectangle = 45 · 25 Substitute 45 for b and 25 for h. = 1,125 Simplify. The area of the lawn is about 353 ft ,125 ft. 2 = 1,478 ft. 2.

PRE-ALGEBRA A pound of grass seed covers approximately 675 ft 2. Find the area of the lawn below. Then find the number of bags of grass seed you need to buy to cover the lawn. Grass seed comes in 3-lb bags. Area of region that is one fourth of a circle: area of circle = r 2 area of quarter circle = r A = (15) 2 Replace r with = exact area Area: Circles LESSON 10-3 Additional Examples ft 2 use 3.14 for.

PRE-ALGEBRA (continued) Area of region that is a rectangle: area of rectangle = bh A = 45 25Replace b with 45 and h with 25. = 1,125 ft 2 The area of the lawn is about 177 ft 2 + 1,125 ft 2 = 1,302 ft 2. You need to buy one 3-lb bags of grass seed. 1,302 ÷ lb. of seed Divide to find the number of pounds of seed. Area: Circles LESSON 10-3 Additional Examples

PRE-ALGEBRA Find the area. 1.Find the exact area of a circle with diameter 32 in. 2.A 5-ft-diameter round table is in a 12 ft-by-15 ft room. a. What is the area covered by the table? Round to the nearest unit. b. What is the area of the rest of the room? Round to the nearest unit. about 160 ft 2 about 20 ft in. 2 Area: Circles LESSON 10-3 Lesson Quiz