Area Module Review PDF

Student Name: Area Module Review Solve each of the following problems. Make sure to show your work. 1. What is the perimeter of the triangle below? Use trigonometry ratios or Special Right Triangle Theorem to solve. Perimeter = 16.7 units 2. What is the perimeter of this triangle? Use the dist...

Student Name: Area Module Review Solve each of the following problems. Make sure to show your work. 1. What is the perimeter of the triangle below? Use trigonometry ratios or Special Right Triangle Theorem to solve. Perimeter = 16.7 units 2. What is the perimeter of this triangle? Use the distance formula to find the side lengths, then add them up. Perimeter = 27.9 units Student Name: Area Module Review 3. What is the perimeter of the rectangle? Use the distance formula to find the missing sides; then, add them together to find the perimeter. Perimeter = 22 units 4. Explain how you would find the perimeter of this triangle. Use trig ratios (tangent and cosine of 51.3 degrees) to find the missing sides. Then add all the side lengths to get the perimeter. Student Name: Area Module Review 5. What is the area of this polygon? 6 𝑐𝑚 8 𝑐𝑚 4 𝑐𝑚 The area of the individual triangles are A1 = (1/2)(8)(6) = 24 cm2 and A2 = (1/2)(8)(4) = 16 cm2. Therefore, the total area of the polygon is A = 24 + 16 = 40 cm2. 6. What is the area of this regular pentagon that has been divided into five congruent triangles? The area of a regular pentagon is the perimeter times half the apothem. Therefore, the area of the pentagon is (5)(8)(6/2) = 120 cm2. Student Name: Area Module Review 7. What is the area of this polygon on a coordinate plane? Divide the polygon into one rectangle and two triangles. The area of the rectangle AR = (4)(2) = 8 square units. The area of one triangle AT = (1/2)(4)(2) = 4 square units. Therefore, the total area of the polygon is Atotal = 8 + 4 + 4 = 16 square units. 8. A family wants to haul two chairs inside their truck, which is 5 feet wide and 8 feet long. Each chair is 3 feet wide and 4 feet high. Can the family haul both chairs at the same time? Show your calculations. Model the vehicle and chairs as rectangles. The approximate area of the vehicle is A = bh = (5)(8) = 40 ft2. The approximate area of one chair is A = bh = (4)(3) = 12 ft2. Therefore, the combined area of both chairs is about 12 + 12 = 24 ft2. Since the combined area of the chairs is less than that of the vehicle, both chairs could be hauled in the vehicle in one trip. Student Name: Area Module Review 𝑛 9. The area of a sector is 𝐴𝑠𝑒𝑐𝑡𝑜𝑟 = 𝜋𝑟 2. What does the variable 𝑛 represent? 360° The variable 𝑛 is the central angle of the sector. 𝑛 𝑛 10. The area of a sector is 𝐴𝑠𝑒𝑐𝑡𝑜𝑟 = 𝜋𝑟 2. What does the term represent? 360° 360° 𝑛 The term represents the ratio of the sector’s central angle to the circle’s total angle. 360° 11. What is the definition for a segment of a circle? A segment is a portion of a sector that is bound by a chord and the minor arc formed by that chord. 12. What is the area of minor sector AOB? 215° 𝑂 𝐴 𝐵 𝑛 𝐴𝐴𝑂𝐵 = 𝜋𝑟 2 360 𝑟 = √32 + 12 = 3.2 𝑛 = 360° − 215° = 145° 145 𝐴𝐴𝑂𝐵 = 3.22 𝜋 = 13 square units 360 Student Name: Area Module Review 13. What is the equation for calculating the area of a triangle? Calculating the area of a triangle is like calculating the area of a rectangle. You multiply the base by the height. However, you divide that value by two (imagine a triangle as half a square). A = ½ base * height 14. If there are 100 men per city block and 2000 blocks in the city, how many men are in the city? We know density = amount/space. Therefore, 100 men/city block = amount of men/2000 blocks. Then, we have that 100 men/city block*2000 blocks = 200000 men. 15. Suppose you cannot identify the known figures in an unknown figure, but you know that its density is 10 objects/square unit and that there are 200 objects in the figure. What is the area of the figure? Because we know density = amount/space, and we know that the density is 10 objects/unit squared and that there are 200 objects in the unit, we have that 200 objects/(10 objects/unit squared) = 20 units squared 16. Name all the ways in which you might calculate the area of an unknown figure. There are a number of ways to go about this. First, we can divide the figure into smaller, known figures. Then, if we calculate the areas of those known figures and sum them up, we’ll have the area of the unknown figure. If that doesn’t work, we can also use context. If we know the density of an object in the figure and the amount of objects in the figure, we can solve for area. Student Name: Area Module Review 17. How many faces, vertices, and edges are in the figure below? To find the faces, count the sides. To find the edges, count the segments. To find the vertices, count the corners. faces = 7, vertices = 7, edges = 12 18. How many faces does a solid with 14 vertices and 21 edges have? Euler’s Theorem would give F+V=E+2 F + 14 = 21 + 2 F + 14 = 21 + 2 F + 14 = 23 F=9 19. Is the shape below a polyhedron? Explain your answer. No, it has a curved side. Polyhedrons have only straight sides. 20. How many edges does a solid with 11 faces and 11 vertices have? Euler’s Theorem would give F+V=E+2 11 + 11 = E + 2 22 = E + 2 20 = E Student Name: Area Module Review 21. Wrapping paper costs $0.025 per square inch. If a moving box that is an 8 ½ inch cube is being wrapped, how much would the wrapping paper for this box cost (rounded to the nearest dollars and cents)? The surface area of the moving box is SA = 6s2. SA = 6(8.5)2 SA = 6(72.25) SA = 433.50 square inches. At $0.025 per square inch, it would take 433.50 x (0.025) or $10.84 to wrap this box. 22. The radius of a salad bowl is 8.9 inches. What is the surface area of the bowl? (Assume the bowl is half a sphere). Use the surface area formula SA = 4(pi)(r2) which results in SA = 4(3.14)((8.9)2)=994.88 square inches. Divide that in half you get 497.44 square inches. 23. Without knowing their diameters, which sporting ball has the smaller surface area--a golf ball or a tennis ball? Explain how you know. Without knowing the diameters, the golf ball would have a smaller diameter than a tennis ball. Given the surface area formula for a sphere, SA = 4 (pi)(r2), the golf ball would have a smaller value for the variable r, which would result in a smaller surface area. 24. A round sea turtle egg measures about 0.5 cm in diameter. What is the surface area of a sea turtle’s egg in square centimeters? Use the surface area for a sphere which is SA = 4(pi)(r2) where r would be ½ (0.5 cm) =.25cm. This yields SA = 4(pi)(r2)=4(3.14)(0.252)=0.785 sq.cm. Student Name: Area Module Review 25. Find the surface area of this regular pyramid. 15 m 4m 6m The area of a regular hexagon can be found by dividing it into 6 congruent triangles. Find the area of one of triangles, then multiply by 6 to find the area B of the base; S=(1/2)Pl + B = 342 m2 26. Find the surface area of this cone. 5m 12m Use Pythagorean Theorem to find the slant height l; then apply S = pi*r(l+r) = 90pi m2 27. Find the surface area of this cone. 5m 4m S = pi*r(l+r) = 36pi m2 Student Name: Area Module Review 28. Find the surface area of this regular pyramid. 6 ft 9 ft S=(1/2)Pl + B = 189 ft2 29. Find the surface area of a rectangular prism with a height of 16 feet, a width of 10 feet, and a length of 13 feet. Set up and solve the following equation: SA = 2B + PH SA = 2(130) + 46(16) SA = 996 ft2 30. Find the surface area of a cube with a side length of 8 m. Set up and solve the following equation: SA = 2B + PH SA = 2(64) + 32(8) SA 384 m2 Student Name: Area Module Review 31. Find the surface area of the triangular prism below. Set up and solve the following equation: SA = 2B + ph SA = 2(24.84) + 21.4(7.3) SA = 205.9 cm2 32. Find the surface area of the rectangular prism below. Set up and solve the following equation: SA = 2B + ph SA = 2(341) + 84(24) SA = 2698 ft2 Student Name: Area Module Review 33. What is the conversion factor from meters to millimeters? There are 1,000 millimeters in a meter. Therefore, the conversion factor is 1,000 millimeters per meter. 34. John is trying to convert an area from meters squared to millimeters squared. He multiplied the area he had by 1,000 and got the wrong answer. What should he have multiplied the original area by? When calculating a unit conversion between units that measure area, we have to remember that the conversion factor needs to be squared. Therefore, we have (1,000 millimeters per meter)2, or 1,000,000 millimeters squared per meter squared. 35. What do we have to do to the conversion factor if we are dealing with units that measure area? Since we multiply units together in order to calculate area, we need to multiply the conversion factor by itself when converting from one unit of area measurement to another. 36. Come up with a singular conversion factor that converts meters squared into inches squared. Be sure to show your work for each step of the process. First, find the conversion factor from meters to feet (3.28084 feet per meter) and square it (10.7639111056 feet squared per meter squared). Now, find the conversion factor from feet to inches (12 inches per foot) and square it (144 square inches per square foot). Now, multiply each square conversion factor together to get 10.7639111056 x 144 = 1550.00319921 inches squared per meters squared. 37. What is the formula for calculating the area of a pyramid? The area of a pyramid is equal to one half the product of the base’s perimeter multiplied by the measure of the slant plus the area of the base. A = (1/2)Pl + B Student Name: Area Module Review 38. If we decrease a dimension on a figure, how is the figure’s area affected? If we decrease a single dimension on a figure, its area necessarily decreases. Imagine the figure shrinking as the dimension is reduced. 39. The building Richard has to clean has dimensions of 7 meters by 7 meters around the base and it is 6 meters high. How much surface area will Richard have to clean? Remember, in this case, we complete the formula and then subtract the area of the base. Therefore, we take 6 x (7 meters)2 and subtract (7 meters)2. This can also be represented as 5 x (7 meters)2. The surface area is 245 meters squared. 40. Richard is asked to spray wash the exterior of a building that is shaped like a cube. He decides to calculate the surface area of the building in order to estimate how much water he will need. He does the calculation using the standard formula and, after doing the job, realizes he overestimated the amount of water he needed. Where was his mistake? Because the exterior of the building does not include the floor, Richard should have subtracted the area of the base from the result he got.