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1-7 PERIMETER, CIRCUMFERENCE, AND AREA (p. 51-58) The investigation can be skipped. The perimeter of a polygon is the sum of the lengths of all of its sides. It is also the total distance around the polygon. The circumference of a circle is also the distance around it. It is equivalent to perimeter in polygons. The area of a polygon or circle is the number of square units that it encloses within its boundary. The boundary is represented by sides or a circular rim. Review the perimeter, circumference, and area formulas on p. 52. You should already be familiar with these formulas for the square, rectangle, and circle. 1. Square P = 4s (where s = side) A s2 2. Rectangle P = 2b +2h (where b = base and h = height) A = bh 3. Circle C d or 2r (where d = diameter and r = radius) A r 2 The units for perimeter and circumference are units to the first power because they represent distances. The units for area are units to the second power or square units because they represent two dimensions. Example: Amy’s garden is a rectangle that is 24 feet long and 16 feet wide. She wants a 3.5 foot cement path around the entire garden. What will be the outside perimeter of the combination garden and path? Make a sketch that shows the rectangles. Do 1 a and b on p. 52. The two formulas for the circle involve the irrational number . What does approximately equal? What kind of decimal does give? If you use the key on your calculator, you will obtain an approximate answer. However, if you leave your answer in terms of , you will get an exact answer. Example: Circle G (show the symbol for circle) has a radius of 6.5 cm. Find the circumference of this circle in terms of . Then, find the circumference to the nearest tenth. Do 2 a and b on p. 53. To find the perimeter of a figure in the coordinate plane, you may need to use both the Ruler Postulate and the Distance Formula. Example: Graph PQR with vert ices P(-2,9), Q(7,-3), R(-2,-3) in the coordinate plane. Find the perimeter of this triangle. If time, do 3 on p. 53. When finding area, you need to use the same unit for each dimension. Example: To make a quilt, you need a rectangular piece of material 36 inches wide and 4 feet long. How many square feet of material do you need? Do 4 on p. 53. How many square feet are there in one square yard? Example: Find the area of a circle whose diameter is 18 cm. Leave your answer in terms of . Do 5 on p. 54. The following two postulates help you find the areas of irregularly-shaped figures. Postulate 1-9: If two figures are congruent, then their areas are equal. Postulate 1-10: The area of a region is the sum of the areas of its nonoverlapping parts. You can find the area of a region by dividing it into multiple rectangles and summing the areas. After briefly examining Ex. 6 on p. 54, do 6 on p. 54. Example: 1 5 ft 5 ft 1 0 ft 1 0 ft 5 ft 5 ft 5 ft 5 ft All of the angles in the above diagram are right angles. Can you find the area of this region by using subtraction? Homework p. 55-58: 4,7,11,15,19,24,29,35,39,42,50,53,58,60,63,64,78,84,86 53. 128 1 512 tiles 4