Lesson 8.1 • Areas of Rectangles and Parallelograms

1 52 CHAPTER 8 Discovering Geometry Practice Your Skills Lesson Areas of Rectangles and ParallelogramsNamePeriodDateIn Exercises 1 4, find the area of the shaded ABCDhas area 2684 m2and width 44 m. Find its a parallelogram with area 85 cm2and an angle with measure 40 .Is your parallelogram unique? If not, draw a different the area the area buys a piece of carpet that measures 20 square yards. Will she beable to completely cover a rectangular floor that measures 12 ft 6 in. by16 ft 6 Explain why or why (4, 5)B(10, 5)C(10, 2)(4, 2)FD(21, 7)(15, 7)EyxP( 4, 3)S( 4, 5)R(7, 1)Q(7, 9)yx13 cm9 cm2 cm2 cm8 cm4 cm4 cm5 cm17 cm1 cm4 cm8 cm4 cm12 11/1/06 1:31 PM Page 52 2008 Kendall Hunt PublishingDiscovering Geometry Practice Your Skills CHAPTER 853 Lesson Areas of Triangles, Trapezoids, and Kites NamePeriodDateIn Exercises 1 4, solve for the unknown 64 ft2,h 126 6 cm,AC 8 cm, and BC 10 the area of the shaded is tangent to circles Mand 16 cm.

2 The radius ofNis 7 cm and the radius ofMis 4 cm. Find the area the area of a parallelogram,ABDEis a kite,AD 18 cm, and BE 10 cm. Find the area (12, 12)(0, 6) RT (6, 0)yxTNMP12 cm20 cm4 cmACBD9 cm2 cm8 cm2 cm8 11/1/06 1:31 PM Page 53 2008 Kendall Hunt PublishingLesson area bundle of hardwood flooring contains 14 12 ft2andcosts $ many square feet of flooring is needed to cover thekitchen and family room? Exclude the fireplace, hearth, andtiled should buy 5% extra flooring to account for many bundles of flooring should you buy? What will be the cost? s Bigtime Bakery has baked the world s largest chocolate cake. It isa rectangular sheet cake that is 600 cm by 400 cm by 180 cm high.

3 Bertwants to apply frosting to the four sides and the top. How many litersof frosting does he need if 1 liter of frosting covers about 1200 cm2? a World Peace Day celebration the students at Cabot Junior/SeniorHigh School are making a 6 m-by-8 m flag. Each of the six grades willcreate a motif to honor the people of the six inhabited three possible ways to divide the flag: one into six congruenttriangles; one into six triangles with equal area but none congruent;and one into six congruent trapezoids. Give measurements or markingson your sketches so each class knows it has equal and Kat are building a kite for the big kite festival. Kit has alreadycut his sticks for the diagonals.

4 He wants to position Pso that he willhave maximum kite area . He asks Kat for advice. What should Kattell him?P13 ft3 ft3 ft 4 ft6 ft18 ft18 ftKitchenTileFamilyroomFireplaceand hearth4 ft7 ft14 ft54 CHAPTER 8 Discovering Geometry Practice Your 11/1/06 1:31 PM Page 54 2008 Kendall Hunt PublishingDiscovering Geometry Practice Your Skills CHAPTER 855 Lesson Areas of Regular Polygons NamePeriodDateIn Exercises 1 3, the polygons are 12 cm cm 6 cm a cmA 197 cm2A cm2A _____a _____p a regular n-gon,s cm,a cm, and A cm2. Find a regular pentagon so that it has a compass and straightedge to perimeter 20 cm. Use the Regular Polygon construct a regular octagon and area Conjecture and a centimeter ruler to its apothem.

5 Use a centimeter ruler to find its approximate its side length and apothem, and use the Regular Polygon area Conjecture tofind its approximate the area of the shaded region between the square and the regular 5 3 11/1/06 1:31 PM Page 55 2008 Kendall Hunt PublishingLesson Areas of CirclesNamePeriodDateIn Exercises 1 4, write your answers in terms of . 9 cm,A cm,A 529 cm2,r 36 cm,A Exercises 5 8, round your answers to the nearest cm,A ,C ,A ,A Exercises 9 and 10, refer to the figure of a circle inscribedin an equilateral triangle. Round your answers to the nearest the area of the inscribed the area of the shaded Exercises 11 and 12, find the area of the shaded region.

6 Write youranswers in terms of . a three circles are cmAC (0, 8)D (8, 0) cma cma56 CHAPTER 8 Discovering Geometry Practice Your 11/1/06 1:31 PM Page 56 2008 Kendall Hunt PublishingDiscovering Geometry Practice Your Skills CHAPTER 857 Lesson any way you slice ItNamePeriodDateIn Exercises 1 6, find the area of the shaded region. Write your answers interms of and rounded to the nearest area is 40 area is 54 area is 51 diameter of the larger circle is 20 cm. Find cmx144 r45 12 cm8 cm3 cm135 8 cm2 cm4 cm120 4 cm5 cm30 11/1/06 1:31 PM Page 57 2008 Kendall Hunt PublishingLesson Surface AreaNamePeriodDateIn Exercises 1 8, find the surface area of each solid. All quadrilaterals arerectangles, and all measurements are in centimeters.

7 Round your answersto the nearest is a regular 6,a , and l bases are square hole in a round is building a museum display case. The sides and bottom will be plywood and the top will be glass. Plywood comes in 4 ft-by-8 ft sheets. How many sheets of plywood will she need to buy? Explain. Sketch a cutting pattern that will leave her with the largest single piece ft2 ft3 ft2 ft1_21 8 Discovering Geometry Practice Your 11/1/06 1:31 PM Page 58 2008 Kendall Hunt Publishing108 ANSWERSD iscovering Geometry Practice Your Skills answer: Lesson Areas of Rectangles and Possible Carpet area is 20 yd2 180 ft2. Room areais ( ft)( ft) ft2. Dana will be26 14 Areas of Triangles, Trapezoids, and 12 cm2 Lesson area Problems1.

8 Bundles; $ cm40 34 cm5 cm40 17 cmLESSON Tessellations with Regular answer: A regular tessellation is atessellation in which the tiles are congruentregular polygons whose edges exactly answer: A 1-uniform tiling is a tessellationin which all vertices are 11/1/06 10:37 AM Page 108 2008 Kendall Hunt PublishingDiscovering Geometry Practice Your Skills cm2 10 135 7 cmLESSON Surface sheet: front rectangle : 3 1 12 4 12 ; back rectangle :3 2 12 7 12 ; bottom rectangle : 3 2 6;side trapezoids: 2 2 8; total 26 of 1 sheet 4 8 32 ft2. Possible pattern: Lesson The Theorem of 21 8 (11, 1);r the base area is 16 cm2, then the radius is 4 radius is a leg of the right triangle; the slantheight is the hypotenuse.

9 The leg cannot be longerthan the 150 in2; hypotenuse QR 25 in.; altitude tothe hypotenuse 12 The Converse of the Pythagorean top triangle is equilateral, so half its side lengthis A triangle with sides , 6, and is a righttriangle because 62 So, the anglemarked 95 should be 90 . cm. By the Converse of the PythagoreanTheorem, ADCis a right triangle, and ADCis aright angle. ADCand BDCare supplementary,so BDCis also a right triangle. Use thePythagorean Theorem to find ft2 ft2 ft3 ft3 ft3 ft1ft1_21ft1_22ft1_22ft1_21ft1_22ft1_2 BackBottomLeft overFrontSideSide2 12 1 12 is too late to change the area . The length of thediagonals determines the Areas of Regular 696 4 cm,a cm,A 28 answer (swill vary):s cm,a cm,A cm2: area of square 36; areaof square within angle 38 36 ; area ofoctagon 120; area of octagon within angle 38 120 45; shaded area 45 cm2 Lesson Areas of or cm211.

10 (64 128) square cm2 Lesson any way you slice It1. 2152 cm2 cm22. 323 cm2 cm2 cm24.(16 32) cm2 cm2 11/1/06 10:37 AM Page 109 2008 Kendall Hunt Publishing