Developing Formulas for Triangles and Quadrilaterals

Problem Solving Developing Formulas for Triangles and Quadrilaterals 1. The area of trapezoid HJKL is 385 mm². Find LM to the nearest tenth. 385 = (1/2)(30 + 23)h 770 = 53h h = 14.5 mm sin 40° = 14 / LM LM = 14 / sin 40° LM = 21.8 mm 2. Samantha is buying stones for a 16 foot by 3 foot walkway. She needs to buy 10% extra for cutting stones for the corners and ends. The stones are rectangles 7 inches long and 4 inches wide and cost $0.97 each. About how much will the stones cost for her walkway? 1   1. 16 ft * 3 ft = 48 ft² = 6912 in² 6912 in² / (7 in * 4 in) = 247.57 stones 247.57 stones * 1.10 = 272.33 stones ≈ 272 stones 272 stones * $0.97/stone = $263.84 3. The length of a rectangular pool is 2 feet less than twice the width. If the area of the pool is 264 ft², what are the dimensions of the pool? (2x - 2)(x) = 264 2x² - 2x - 264 = 0 2(x - 12)(x + 11) = 0 x = 12 Dimensions: 22 ft by 12 ft 4. Find the area of the kite. Round to the nearest tenth. 2.3 cm 4 cm 4 cm (2.3)² + y² = 4² 5.29 + y² = 16 y² = 10.71 y = 3.3 cm A = (1/2)(11.5)(4.6) A = 26.5 cm² 1. What is the area of the regular nonagon? Round to the nearest tenth.   A = (1/2)(10.99)(70) A = 384.7 cm² 2. The top view of a two-tiered wedding cake is shown. Each tier is a regular hexagon. What percent of the bottom tier is covered by the top tier? Round   to the nearest percent. Small tier: (1/2)(30)(2.5√3) = 64.95 cm² Big tier: (1/2)(42)(4√3) = 143.94 cm² (64.95 / 143.94) * 100% = 45% 3. When diving and snorkeling, you should leave a "radius of approach," or a restricted area around certain animals that live in the waters where you are diving. How much greater is the restricted   area around a monk seal than the restricted area around a sea turtle? Give your answer in terms   of π. Animal Radius of Approach sea turtle 20 ft monk seal 100 ft π(100²) - π(20²) = 9600π ft² 4. A yield sign is a regular triangle and is available in two sizes: 30 inches or 36 inches. Find how much more metal is needed to make a 36 inch sign than a 30 inch sign. Answer to the nearest percent.   36 in sign: (1/2)(36)(18√3) = 561.12 in² 30 in sign: (1/2)(30)(15√3) = 389.71 in² (561.12 - 389.71) / 389.71 * 100% = 44% **Choose the best answer.** 5. A regular hexagon has an apothem of 4.6 centimeters. Which is the best estimate for the area of the hexagon? A. 36.7   cm² B. 63.5 cm² C. 148.8 cm² D. 540.0 cm² 6. An amusement park ride is made up of a large circular frame that holds 50 riders. The circumference of the frame is about 138 feet. What is the diameter of the ride to the nearest foot?   A. 22 ft B. 44 ft C. 69 ft D. 138 ft 7. A cyclist travels 50 feet after 7.34 rotations of her bicycle wheels. What is the approximate diameter of the wheels? A. 13 in. B. 24 in. C. 26 in. D. 28 in.   1. Find the shaded area. Round to the nearest tenth. Area = (1/2)(9.5)(8.5) = 40.375 cm² Area = (1/2)(12)(8.5) = 51 cm² Total Area = 40.375 + 51 = 91.375 cm² ≈ 91.4 cm² 2. Jessica is painting a bedroom wall shown by the shaded area below. The cost of paint is $6.90 per quart, and each quart covers 65 square feet. What is the total cost of the paint if she applies two coats of paint to the   wall? Area = (1/2)(9)(10) = 45 ft² Total Area = 2 * 45 ft² = 90 ft² 90 ft² * (1 quart / 65 ft²) * $6.90/quart = $9.54 Choose the best answer. 3. Enchanted Rock State Natural Area in Fredericksburg, Texas, has a primitive camping area called Moss Lake. Which is the best estimate for this area if the length of each grid square is 10   meters? [Image of a map with a shaded area representing Moss Lake] A. 600 m² B. 3200 m² C. 5400 m² D. 8000 m² 4. Find the area of the section of basketball court that is shown. Round to the nearest tenth. F. 612.7 ft² G. 1225.4 ft² H. 2450.8 ft² J. 4901.6 ft² 5. Find the shaded area. Round to the nearest tenth. 18 mm 12 mm | 15 mm Area = (1/2)(12)(15) = 90 mm² Area = (1/2)(18)(7.2) = 64.8 mm² Total Area = 90 + 64.8 = 154.8 mm² 6. Which is the best estimate for the area of the pond? Each grid square represents 4 square feet. [Image of a pond on a grid] F. 24 ft² G. 48 ft² H. 96 ft² J. 120 ft²