Area of Regular Polygons

Transcription

1 Area of Regular Polygons Name:_ Find the area of each regular polygon. Leave your answer in simplest (radical) form. If your answer does not have a radical form, then round to the nearest tenth ) 2.) 3.) ) 16 3 un 2 2.) un 2 3.) 696 un 2 4.) 5.) 6.) ) 95.6 un 2 5.) 792 un 2 6.) un 2 7.) Pentagon 8.) Triangle 9.) 7-gon apothem = 7.3 apothem = 14 apothem = 21.8 side = 10.6 side = 28 3 side = un Area = _ un Area = _ un Area = 2 Use what you know about special right triangles to solve for the area of each regular polygon un 10.) un 11.) un 12.) 2 13.) Find the perimeter of a regular hexagon that has an area of 54 3 ft2 units. P = 36 units 14.) Can a regular octagon have an area of 10 units2? Why or why not? Yes - any regular polygon can have any value as an area as long as that value is positive.

2 Area and Perimeter of Composite Figures Calculate the area of each figure. 4cm 32cm 6cm 12cm 5cm 1.) 37.8 cm 2 2.) cm For each composite figure shown *Determine the total perimeter *Determine the total area 11 mm 8cm 6m 2m 15 mm 9 mm 14cm 3.5cm 4m 3.) Perimeter: 51 cm 4.) Perimeter: m 5.) Perimeter:_ 114 mm Area: 77 cm 2 Area: 20 m 2 Area: 396 mm 2 The design of a machine part is shown to the right. The cut-out shape is a quarter circle π cm 2 Area: π cm Perimeter: 10cm 20cm

3 Pre - AP Geometry Area of Parallelograms and Triangles Name: Date: Class Pd. _ Find the perimeter and area of each triangle or parallelogram. Make certain to use appropriate units. Round to the nearest tenth. 8 1.) 2.) 4 3.) 10 3 A= 16 3 units 2 A= 6 units 2 A= 35 units 2 P = 24 units P = 12 units P = units ) 2 5.) 6.) 3 ft 2 ft 60 o 45 o 2 \ \ x 8x A= 4 units A= 3 3 ft 2 A= 32 2 un 2 P = 8 units P = 10 units P = 36 2 units 7.) The height of a parallelogram is 5 ft more than its base. If the area of the parallelogram is 204 square feet, find its base and height. Base = _ 12 Height: _ 17 8.) The base of a triangle is four times its height. If the area of the triangle is 242 square millimeters, find its base and height. Base: 44 Height: 11 9.) Assume the triangle from problem #8 is a right triangle. Find the measure of the two acute angles. 14 o 76 o Angle 1: Angle 2:

4 10.) Three stakes are being planted at different vertices. Stake A is at (-4, 4) and Stake B is at (-2,-2). a.) What are two possible locations for Stake C in order for the three stakes to form a right triangle? Option 1: (1, -1) Option 2: (4, 0) Any point on a 1/3 slope from either stake. b.) What is the area in square units of the two right triangles that result from the possibilities you found in part a? Area = Answers will vary. Use distance formula from each point you chose. 11.) A concrete sidewalk made up of adjacent parallelograms is shown below. 106" 106" 100" 102in. 48" 128" a.) Find the total area of this section of sidewalk. Area = 49,776 in 2 b.) Find the perimeter of the outside of the section of sidewalk. Perimeter = 1180 in Use the figure to the right for exercise 12. 2x + 1 x 12. a) Solve for x if the area of the entire figure is 350 ft 2. x 2.7 ½x b.) What is the area of the shaded region only in sq. ft.? Area ft 2

5 Pre-AP Geometry Name: Area of Trapezoids, Rhombi and Kites Date: _ Class Pd. _ Find the area and perimeter of the trapezoid, rhombus or kite. 3 1.) 6 2.) 3.) un 2 48 un 2 18 un 2 A = A = A = 42.9 units 40 units units (typo on P = P = P = yours, my bad) 4.) A trapezoid has base lengths of 19.5 and 24.5 cm with an area of 154 cm 2. What is the height of the trapezoid? 7 cm Height = 5.) One diagonal of a kite is twice as long as the other diagonal. If the area of the kite is 400 m 2, what are the lengths of the diagonals? 20 m 40 m d 1 = d 2 = 6.) 16 congruent rhombi-shaped tiles are used above a kitchen sink as a back splash (shown below). The length of the design is 27 total inches and the total area is 108 in 2. a.) Find the area of one of the tiles in 2 Area = b.) Find the length of each diagonal. 4.5 in 3 in d 1 = d 2 = c.) What is the perimeter of the entire pattern? P = inches *d.) Write an equation to determine the perimeter (P) of the pattern if x number of tiles are used. Bonus - I'll tell you later... If you really care... P =

6 Using the space below, draw me a pretty picture of something that makes you happy.

7 Pre - AP Geometry Name: Area of Circles and Sectors Date: Class Pd._ Find the area and circumference of the circle. Write your answers in terms of pi. 1.) 2.) 4 2 in 3.) 18ft. 11 mi A = 324π ft sq A = 16π in sq A = 30.25π mi sq C = 36 π ft C = 8π in C = 11π mi 4.) The area of a circle is square centimeters. What is the diameter? d = 14 cm 5.) What is the area of a sector with a central angle of 50 o on a circle with a radius of 12 mm? A = 20π mm sq 6.) What is the area of a sector with a central angle of 315 o on a circle with a radius of 3 in? A = in sq 7.) If a pie plate has 12 inch diameter, how much area will ¾ of the crust cover? A = 27π 8.) A circular pool and a sidewalk around it create concentric circles. The sidewalk is 3ft wide and the diameter of the pool is 20 ft. a.) What is the radius of the outer circle? 13 ft r = b.) If you wanted a tarp to cover the pool and the sidewalk, what would the diameter of the tarp need to be? d = 26 ft c.) What is the minimum area of the tarp to cover the pool and the sidewalk? A = 169π or ft sq

8 Using the space below, draw me a pretty picture of something that makes you sad.

9 Pre - AP Geometry Name: Areas of Similar Figures Date: Class Pd. _ 6 For each pair of figures, find the area of the shaded figure. Round your answer to the nearest tenth. 1.) 2.) 6ft 3.) ft 15 A = 20 in 2 A = 8550cm 2 A = 12m 2 A = 1.3 m sq A = 180 in sq A = cm sq For each pair of figures, find the scale factor of LARGE:SMALL. Then, solve for x. 4.) x 5.) 12ft x 6.) 9.5 A = 16 in 2 A = 10ft 2 A = 71 in 2 A = 360ft 2 x A = 81π yd 2 2 yd A = 4π yd 2 19 : 9 Scale: 6 : 1 Scale: 9 : 2 Scale: 4.5 x = 2 x = 9 x = 7.) Matt is drawing two scale models of the floor plans of a house of two different sized poster boards. The length of the larger poster is 11 inches. The length of the smaller poster is 6 inches. a.) What is the area of the smaller poster if the area of the larger poster is 93.5 in 2? 27.8 in sq A = b.) What is the width of the larger poster? 8.5 in w = c.) What is the width of the smaller poster? 4.36 w = d.) If Matt's house takes up the entire large poster, what is the square footage of his house if he uses the scale ¼" = 1 ft? A = 1496 sq.ft.

10 This one's for real. Using the columns below, give me some feedback as to how Pre-AP Geometry has been good as well as ways that I could improve as an instructor. And don't try to suck up to me. Your grade will be the grade that you earn. I am looking for honest feedback. If you have nothing nice to say, that sucks for me, but I get it. Good stuff Get better at stuff

11 Pre-AP Geometry Name: _ Surface Area of Prisms and Cylinders Date: Class Pd._ Find the Lateral Area and Surface Area of each prism or cylinder. Round to the nearest tenth or leave your answer in terms of pi. 1in 7m 1.) 2.) 3.) 21m 4ft 3ft 10ft 4in 3in 12in SA = 132 ft sq SA = in sq SA = 392π m sq LA = 120 ft sq LA = in sq LA = 294π m sq 4.) 4in 5.) 6.) 4ft 4in 9.5in \ / 11m 5in / \ 2m SA = 139 in sq SA = m sq SA = 42π ft sq LA = in sq LA = 132 m sq LA = 24π ft sq 3ft A 3-tier wedding cake is made by placing one cake atop another atop another. All three cakes have a height of 18 inches. The top cake has a radius of 18 inches, the middle has a radius of 36 inches and the bottom has a radius of 54 inches. a.) What is the total area that will get icing? (Visible area) A = 6804π in sq OR 21,375 in sq b.) If the icing costs $.08 for every 3 square inches, how much will this cake cost to ice? c = $570.01

12 Pre-AP Geometry Name: _ Volume of Prisms and Cylinders Date: Class Pd._ Find the Volume of each prism or cylinder. Round to the nearest tenth or leave your answer in terms of pi. 1in 7m 1.) 2.) 3.) 21m 4ft 3ft 10ft 4in 3in 12in V = 60 ft cu. V = 96 in cu. V = 1029π m cu. 4.) 4in 5.) 6.) 4ft 4in 9.5in \ / 11m 5in / \ 2m 74.2 in cu m cu OR m cu 36π ft cu. V = V = V = 3ft A 3-tier wedding cake is made by placing one cake atop another atop another. All three cakes have a height of 18 inches. The top cake has a radius of 18 inches, the middle has a radius of 36 inches and the bottom has a radius of 54 inches. a.) What is the total volume of the wedding cake? V = 81648π inches cubed b.) If the cake costs $.08 for every 3 cubic inches, how much will this cake cost? c = $6,840.13

13 Pre-AP Geometry Name: _ Surface Area of Pyramids and Cones Date: Class Pd._ Find the Lateral Area and Surface Area of each pyramid or cone. Round to the nearest tenth or leave your answer in terms of pi. 1.) 2.) 3.) 20cm / \ 45 o 5cm 50ft SA = cm sq SA = ,000 2 ft sq SA = 196π m sq LA = 150 cm sq LA = 10,000 2 ft sq LA = 147π m sq 21m 7m 4.) 5.) 9m 12ft 10m 14ft 397 m sq SA = 225 m sq LA = ft sq SA = ft sq LA = 6.) Find the surface area and lateral area of a cone if the height is 14 cm and the slant height is 16.4cm π OR cm sq SA = 193.4π OR cm sq LA = 7.) The roof of a gazebo is a regular octagonal pyramid. The base of the pyramid has sides of 0.5m and the slant height of the roof is 1.9m. a.) Find the area of the roof only. A = b.) If roofing shingles cover and area of.25m 2, and cost $1.89 each, how much will it cost to shingle the roof? Cost = 3.8 m sq $28.73

14 Pre-AP Geometry Name: _ Volume of Pyramids and Cones Date: Class Pd._ Find the Volume of each pyramid or cone. Round to the nearest tenth or leave your answer in terms of pi. 1.) 2.) 3.) 20cm \ 45 o 5cm 50ft / V = 71.5 cm cu V = 16,666.7 ft cu V = 686π m 7m 4.) 5.) 9m 12ft 10m 14ft m cu V = 784 ft cu V = 6.) The part of a dish that holds ice cream is in the shape of an upside down cone. The base of the cone has a radius of 3 inches and the height is 1.8 inches. 3in a.) What is the volume of the cone? V = 5.4π OR 17 in cu 1.8in 7.) A stage has the form of a square pyramid with the top sliced off along a plane parallel to the base. The side length of the top square is 12ft and the side length of the bottom square is 16ft. The height of the stage is 3ft. a.) What is the volume of the entire pyramid that the stage is OR 763 ft cu part of? V = 3 b.) What is the volume of the top of the pyramid that OR 322 ft cu is removed? V = c.) What is the volume of the stage? ft cu V = 16ft 12ft 3ft

15 Pre-AP Geometry Name: _ Surface Area and Volume of Spheres Date: Class Pd._ Find the Surface area and Volume of each sphere or hemisphere. Leave your answer in terms of pi. 1.) 2.) 3.) 5ft 6in 32ft SA = 100π ft sq SA = 72π in sq SA = 1024π ft sq V = 500π ft cu V = 144π in cu V = 16384π ft cu ) Find the Surface area and volume of each sphere or hemisphere with the given characteristics. Lave your answer in terms of pi. a.) Hemisphere: diameter of 48 yd. SA = 1152π yd sq V = 9216π yd cu b.) Sphere: Circumference of great circle (Equator) = 24π miles. SA = _ 576π mi sq V = 2304π mi cu 5.) The sphere at the right fits snugly into the cube so that the sphere touches the cube at one point on each side. The side length of the cube is 12in. a.) What is the surface area of the cube? SA = 864 in sq b.) What is the surface area of the sphere? SA = 144π in sq c.) What is the ratio of the volume of the cube to the volume of the sphere? Ratio = π 6.) Saturn's biggest moon, Titan has a radius of about 2575 kilometers. What is the approximate surface area and volume of Titan? SA = 26,522,500π or 83,32, mi sq V = 2.28 x mi cu