CHAPTER 12: PERIMETER, AREA, CIRCUMFERENCE, AND 12.1 INTRODUCTION TO GEOMETRIC 12.2 PERIMETER: SQUARES, RECTANGLES,

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1 CHAPTER : PERIMETER, AREA, CIRCUMFERENCE, AND SIGNED FRACTIONS. INTRODUCTION TO GEOMETRIC MEASUREMENTS p. -3. PERIMETER: SQUARES, RECTANGLES, TRIANGLES p AREA: SQUARES, RECTANGLES, TRIANGLES p CIRCUMFERENCE: CIRCLES p AREA: CIRCLES p SIGNED FRACTIONS p. -3 ANSWER KEY P. 4-5

2 . INTRODUCTION TO GEOMETRIC MEASUREMENTS Key Vocabulary. side: length: l width: w height: h base: radius: b diameter: circumference: perimeter: area:

3 . PRACTICE EXERCISES Label the following using geometric terms and provide definition. ) l ) 3 w 4) h 5) b 6) ) 8) 9) 0) 3

4 . FINDING PERIMETERS: SQUARES, RECTANGLES, AND TRIANGLES Think. Examples of perimeter measurements include fences, floorboards, and out of bounds lines on an athletic field or court. There are different perimeter formulas, for squares, rectangles, and triangles. Square: The sides on squares are labeled with an s. o Formula: Perimeter (P) = side (s) times 4 or 4s. If s = 4 in, the P = 4(4) or 6 in. Rectangle: The sdes on rectangles are labeled length ( l ) and width (w). o Formula: Perimeter (P) = times length ( l ) plus width (w) or (l+w). o If l = 6 ft and w = 5 ft, P = (6+5) or ft. Triangle: The sides on triangles are labeled a, b, and c. o Formula: Perimeter (P) is side a + side b + side c or a + b + c. o If a = cm, b = 5 cm, and c = cm, P = or 4 cm. Try It. Write the formulas and find the perimeters. Label the units. Square Formula Perimeter ) s = 8 cm ) s = 0 miles Rectangle 3) l = 6 ft, w = ft 4) l = 8 in, w = 4 in Triangle 5) a = 4 yd, b = 5 yd, c = 8 yd 6) a = 0 cm, b = 4 cm, c = 6 cm 4

5 . Practice Exercises Write formula and find the perimeters for the following geometric shapes. Be sure to label the units. Formula Perimeter Squares ) side = ft ) side = 3 yd 3) side = 0 m Rectangles 4) l = 3 cm, w = 4 cm 5) l = 6 yd, w = 4 yd 6) l = 0 miles, w = 8 miles Triangles ) a = ft, b = 4 ft, c = 3ft 8) a = 6 in, b = 9 in, c = 4 in 9) a = yd, b = 8 yd, c = 0 yd 0) A triangle has sides a = x, b = 3x + 4, and c = x + x + 3. Simplify to write the perimeter of the triangle. Draw a picture and label sides. 5

6 .3 FINDING AREAS: SQUARES, RECTANGLES, AND TRIANGLES Key Vocabulary. square units: Think.3 Examples of area measurements include flooring, lawns, and counter space. Area formulas a different for squares, rectangles, and triangles. Square: Area (A) = side (s) squared or s o If s = 5 ft, the area = 5 = 5 square feet or 5ft. Rectangle: Area (A) = length( l ) times width (w) or lw o If l = 8 ft and w = ft, the area = 8. = 56 ft. Triangle: Area (A) = base (b) times (h) or bh or bh o If b = 6 cm and h = 9 cm, the area = (6)(9) 54 = (54) cm. Try It.3 Write the formulas and find the areas. Be sure to label units. Square Formula Area ) s = 8 miles ) s = 0 feet Rectangle 3) l = 4 in, w = in 4) l = 6 m, w = 4 m Triangle 5) b = 9 cm, h = 8 cm 6) b = yd, h = 6 yd 6

7 .3 PRACTICE EXERCISES Write the formulas and find the areas. Be sure to label the units. Square Formula Area in unit ) s = 6 in ) s = 4 yd 3) s = m Rectangle 4) l = 6 ft, w = 4 ft 5) l = 8 cm, w = 3 cm 6) l = 0 miles, w = miles Triangle ) b = 4 yd, h = 5 yd 8) b = 8 in, h = 6 in 9) b = 9 mm, h = 8 mm 0) You are planning to pour a concrete slab for a new house foundation. The slab will be poured in 4 sections. Find the total area for the concrete slab. 8 ft 8 ft A B 8 ft C D 8 ft

8 .4 CIRCUMFERENCE: CIRCLES Key Vocabulary.4 diameter (d): radius (r): circumference (C): pi (π): Think.4 Examples of circumference measurements include the distance around the edge of a coin or a rim of a cup. To find the circumference, you need two values. o Pi (π) = 3.4 or AND diameter(d) OR radius (r) o diameter (d) = radius (r) time or r o radius = d or d Circumference Formulas o C = πr or C = πd o Use Pi = 3.4 and r = 6 ft C = πr C = ()(3.4)(6) = 3.68 ft. C = πd C = (3.4) () = 3.68 ft. o Use Pi = and r = ft C = πr C = πd Try it.4 Find the diameter or radius 44 C= 4 44 C= ) If d = ft, then r = ) If r = 6 cm, then d = Find the circumference (C) when π = 3.4 3) If r = 6 ft, C = 4 ) If d = 8 yd, C = Find the circumference (C) when 5) If d = 4 m, C = 6) If r = 3.5 mm, C = 8

9 .4 PRACTICE EXERCISES Find the diameter or radius. ) If d = in, then r = ) If r = 8 ft, then d = 3) If d = 5 yd, then r = 4) If r = 3.5miles, then d = 5) If d = 5 mm, then r = Find the circumference (C) when π = ) If r = 6 cm, then C = ) If r = 4 m, then C = 8) If d = 8 km, then C = Find the circumference (C) when. 9) If d = 4 in, then C = 0) If r = 3.5 ft, then C = 9

10 .5 AREA: CIRCLES Think.5 Examples of area measurements for circles include the face of a coin, the surface of a plate, and the space watered by a circular sprinkler. To find the area (A) for s circle, you need two values. o Pi (π) = 3.4 or AND diameter(d) OR radius (r) o Diameter (d) Radius (r) time or r o Radius (r) = d diameter or d The formula for the area (A) of a circle is πr : o 3.4(r ) or ( ) r Using Pi = 3.4 o If r = 5 ft, the area (A) is 3.4(5 ) = 3.4(5) = 8.5 ft or 8.5 square feet Using o If d = in, the area is Pi (36) 3in o If r = ft, the area (A) is 54 54f t Try It.5 Write the formula and find the area. Be sure to label the units. Use pi = 3.4. Formula Area ) r = 4 in ) r = 8 miles 3) d = 8 yd 4) d = 0 ft Use pi =. 5) r = cm 6) d = mm 0

11 .5 PRACTICE EXERCISES Write the formula and find the area. Be sure to label the units. Use pi = 3.4. Formula Area ) r = 6 cm ) r = 8 in 3) d = ft 4) d = yd 5) r min Use pi 6) r = 4 m ) r = yd 8) d = 84 in 9) r = 49 cm 0) A radio station broadcasts from a single tower. The radius of the signal is 8 miles. What is the area covered for the broad cast? Formula: Area

12 .6 SIGNED FRACTIONS Key Vocabulary.6 signed fraction: Think.6 When adding fractions with unlike signs, find a common denominator then use a T-chart to find the difference. Keep the sign of the larger fraction = 4 = 6 When subtracting fractions with unlike signs, rewrite the equation using addition then use a T-chart to find the difference. Keep the sign of the larger fraction When add or subtracting 3 or more signed fractions, combine the like signs first. Think Combine Rewrite: Add or subtract the signed fractions. Reduce fractions as needed. ) 3 = ) 3 = 4 8 3) 4 = 4) =

13 .6 PRACTICE EXERCISES Add or subtract the signed fractions. Reduce fractions as needed. ) = ) = 3) 3 6 = 4) = 5) 6) ) 8) 4 8 = 5 = = = 8 4 9) = 5 0 0) 5 5 = 3 6 3

14 Chapter Answer Key. ) side ) length 3) width 4) height 5) base 6) radius ) diameter ) 6 yd 3) 44 m 4) 4 ft 5) 4 cm 6) 0 square miles or miles ) 0 yd 8) 4 in 9) 36 mm 0) 66 ft 8) circumference 9) area. ) 8 ft ) yd 3) 40 m 4) 4 cm 5) 0 yd 6) 36 miles ) 9 in 8) 9 in 9) 30 yd.4 ) r= in ) d= 36 ft 3) r=.5 yd 4) d= miles 5) =.5 mm 6) 3.68 in ) 5. ft 8) 5. m 9) 44 cm 0) ft 0) x + 6x +.3 ) 36 in 4

15 .5 )3.04 cm ) in 3) ft 4) 3.04 yd 5) 9.65 mm 6) 6.6 m ) 54 yd 8) 5, 544 in 9), 546 cm 0) square miles.6 ) ) 3) 4) 3 5) 6) ) 8) 9) 0) 3 5