Geometry SIA #3. Name: Class: Date: Short Answer. 1. Find the perimeter of parallelogram ABCD with vertices A( 2, 2), B(4, 2), C( 6, 1), and D(0, 1).

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1 Name: Class: Date: ID: A Geometry SIA #3 Short Answer 1. Find the perimeter of parallelogram ABCD with vertices A( 2, 2), B(4, 2), C( 6, 1), and D(0, 1). 2. If the perimeter of a square is 72 inches, what is its area? 3. The figure is formed from rectangles. Find the total area. The diagram is not to scale. 4. Is TVS scalene, isosceles, or equilateral? The vertices are T(1,1), V(4,0), and S(3,5). 5. A quadrilateral has vertices (2, 2), (2, 2), ( 1, 2), and ( 1, 2). What special quadrilateral is formed by connecting the midpoints of the sides? 6. In the coordinate plane, three vertices of rectangle HIJ K are H(0, 0), I(0, d), and K(e, 0). What are the coordinates of point J? 1

2 Name: ID: A Find the length of the missing side. The triangle is not drawn to scale A triangle has side lengths of 28 in, 4 in, and 31 in. Classify it as acute, obtuse, or right. 9. Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tenth. 10. The area of a square garden is 242 m 2. How long is the diagonal? 11. Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form. 12. A piece of art is in the shape of an equilateral triangle with sides of 13 in. Find the area of the piece of art. Round your answer to the nearest tenth. 13. Find the missing value to the nearest hundredth. 14. Find the missing value to the nearest hundredth. 2

3 Name: ID: A 15. Find the missing value to the nearest hundredth. 16. Use a trigonometric ratio to find the value of x. Round your answer to the nearest tenth. 17. Find the value of x. Round to the nearest tenth Viola drives 170 meters up a hill that makes an angle of 6 with the horizontal. To the nearest tenth of a meter, what horizontal distance has she covered? 3

4 Name: ID: A Find the value of x. Round to the nearest degree Find the value of x to the nearest degree To approach the runway, a pilot of a small plane must begin a 9 descent starting from a height of 1125 feet above the ground. To the nearest tenth of a mile, how many miles from the runway is the airplane at the start of this approach? 24. Given a regular hexagon, find the measures of the angles formed by (a) two consecutive radii and (b) a radius and a side of the polygon. 4

5 Name: ID: A 25. The area of a regular hexagon is 35 in. 2 Find the length of a side. Round your answer to the nearest tenth. 26. You are planning to use a ceramic tile design in your new bathroom. The tiles are blue-and-white equilateral triangles. You decide to arrange the blue tiles in a hexagonal shape as shown. If the side of each tile measures 7 centimeters, what will be the exact area of each hexagonal shape? 27. Find the area of a regular hexagon with side length of 8 m. Round your answer to the nearest tenth. Find the area of the regular polygon. Give the answer to the nearest tenth. 28. pentagon with a side of 10 cm Find the area of the triangle. Give the answer to the nearest tenth. The drawing may not be to scale Use Euler s Formula to find the missing number. Faces: 25 Vertices: 17 Edges:? 31. Mario s company makes unusually shaped imitation gemstones. One gemstone had 12 faces and 10 vertices. How many edges did the gemstone have? 5

6 Name: ID: A Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number Find the surface area of the cylinder to the nearest whole number. 34. The radius of the base of a cylinder is 39 in. and its height is 33 in.. Find the surface area of the cylinder in terms of. 35. Find the surface area of the pyramid shown to the nearest whole number. 6

7 Name: ID: A 36. Find the slant height x of the pyramid shown, to the nearest tenth. 37. Find the surface area of the cone in terms of. 38. The lateral area of a cone is 558 cm 2. The radius is 31 cm. Find the slant height to the nearest tenth. 39. Find the volume of the given prism. Round to the nearest tenth if necessary. 40. Concrete can be purchased by the cubic yard. How much will it cost to pour a slab 18 feet by 18 feet by 4 inches for a patio if the concrete costs $41.00 per cubic yard? 7

8 Name: ID: A Find the volume of the cylinder in terms of Find the volume of the composite space figure to the nearest whole number. 43. Find the volume of the square pyramid shown. Round to the nearest tenth if necessary. 8

9 Name: ID: A Find the volume of the cone shown as a decimal rounded to the nearest tenth A balloon has a circumference of 11 cm. Use the circumference to approximate the surface area of the balloon to the nearest square centimeter. 46. Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit. 47. The volume of a sphere is 1928 m 3. What is the surface area of the sphere to the nearest tenth? Are the two figures similar? If so, give the similarity ratio of the smaller figure to the larger figure Find the similarity ratio of a cube with volume 216 ft 3 to a cube with volume 1000 ft The surface areas of two similar solids are 384 yd 2 and 1057 yd 2. The volume of the larger solid is 1795 yd 3. What is the volume of the smaller solid? 9

10 Geometry SIA #3 Answer Section SHORT ANSWER 1. ANS: 22 units PTS: 1 DIF: L3 REF: 1-8 Perimeter, Circumference, and Area OBJ: Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5 MA.912.G.6.5 TOP: 1-8 Problem 3 Finding Perimeter in the Coordinate Plane KEY: perimeter coordinate plane Distance Formula 2. ANS: 324 in. 2 PTS: 1 DIF: L3 REF: 1-8 Perimeter, Circumference, and Area OBJ: Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5 MA.912.G.6.5 TOP: 1-8 Problem 4 Finding Area of a Rectangle KEY: area square 3. ANS: 68 ft 2 PTS: 1 DIF: L2 REF: 1-8 Perimeter, Circumference, and Area OBJ: Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5 MA.912.G.6.5 TOP: 1-8 Problem 6 Finding Area of an Irregular Shape KEY: area rectangle 4. ANS: scalene PTS: 1 DIF: L2 REF: 6-7 Polygons in the Coordinate Plane OBJ: Classify polygons in the coordinate plane STA: MA.912.G.1.1 MA.912.G.2.6 MA.912.G.3.1 MA.912.G.3.3 MA.912.G.4.1 MA.912.G.4.8 TOP: 6-7 Problem 1 Classifying a Triangle KEY: triangle distance formula isosceles scalene 5. ANS: rectangle PTS: 1 DIF: L3 REF: 6-7 Polygons in the Coordinate Plane OBJ: Classify polygons in the coordinate plane STA: MA.912.G.1.1 MA.912.G.2.6 MA.912.G.3.1 MA.912.G.3.3 MA.912.G.4.1 MA.912.G.4.8 TOP: 6-7 Problem 3 Classifying a Quadrilateral KEY: midpoint kite rectangle 1

11 6. ANS: (e, d) PTS: 1 DIF: L2 REF: 6-8 Applying Coordinate Geometry OBJ: Name coordinates of special figures by using their properties STA: MA.912.G.1.1 MA.912.G.2.6 MA.912.G.3.3 MA.912.G.3.4 MA.912.G.4.8 MA.912.G.8.5 TOP: 6-8 Problem 2 Using Variable Coordinates 7. ANS: 7 KEY: coordinate plane algebra rectangle PTS: 1 DIF: L3 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: Use the Pythagorean Theorem and its converse STA: MA.912.G.5.1 MA.912.G.5.4 MA.912.G.8.3 TOP: 8-1 Problem 2 Finding the Length of a Leg KEY: Pythagorean Theorem leg hypotenuse DOK: DOK 1 8. ANS: obtuse PTS: 1 DIF: L3 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: Use the Pythagorean Theorem and its converse STA: MA.912.G.5.1 MA.912.G.5.4 MA.912.G.8.3 TOP: 8-1 Problem 5 Classifying a Triangle KEY: right triangle obtuse triangle acute triangle DOK: DOK 1 9. ANS: x = 9.9, y = 7 PTS: 1 DIF: L4 REF: 8-2 Special Right Triangles OBJ: Use the properties of and triangles STA: MA.912.G.5.1 MA.912.G.5.3 MA.912.G.5.4 TOP: 8-2 Problem 2 Finding the Length of a Leg KEY: special right triangles hypotenuse leg DOK: DOK ANS: 22 m PTS: 1 DIF: L4 REF: 8-2 Special Right Triangles OBJ: Use the properties of and triangles STA: MA.912.G.5.1 MA.912.G.5.3 MA.912.G.5.4 TOP: 8-2 Problem 3 Finding Distance KEY: special right triangles diagonal 11. ANS: 6 3 PTS: 1 DIF: L2 REF: 8-2 Special Right Triangles OBJ: Use the properties of and triangles STA: MA.912.G.5.1 MA.912.G.5.3 MA.912.G.5.4 TOP: 8-2 Problem 4 Using the Length of One Side KEY: special right triangles leg hypotenuse 2

12 12. ANS: 73.2 in. 2 PTS: 1 DIF: L2 REF: 8-2 Special Right Triangles OBJ: Use the properties of and triangles STA: MA.912.G.5.1 MA.912.G.5.3 MA.912.G.5.4 TOP: 8-2 Problem 5 Applying the 30º-60º-90º Triangle Theorem KEY: area of a triangle word problem problem solving 13. ANS: PTS: 1 DIF: L3 REF: 8-3 Trigonometry triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 3 Using Inverses KEY: angle measure using tangent DOK: DOK ANS: 60 PTS: 1 DIF: L3 REF: 8-3 Trigonometry triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 3 Using Inverses KEY: angle measure using cosine DOK: DOK ANS: 4.59 PTS: 1 DIF: L3 REF: 8-3 Trigonometry triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 3 Using Inverses KEY: angle measure using sine DOK: DOK ANS: 24.7 PTS: 1 DIF: L2 REF: 8-3 Trigonometry triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 2 Using a Trigonometric Ratio to Find Distance KEY: side length using tangent tangent tangent ratio 17. ANS: 8.1 PTS: 1 DIF: L3 REF: 8-3 Trigonometry triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 2 Using a Trigonometric Ratio to Find Distance KEY: cosine side length using sine and cosine cosine ratio 3

13 18. ANS: 31.4 PTS: 1 DIF: L3 REF: 8-3 Trigonometry triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 2 Using a Trigonometric Ratio to Find Distance KEY: sine side length using sine and cosine sine ratio 19. ANS: m PTS: 1 DIF: L3 REF: 8-3 Trigonometry triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 2 Using a Trigonometric Ratio to Find Distance KEY: cosine word problem side length using sine and cosine problem solving cosine ratio 20. ANS: 44 PTS: 1 DIF: L3 REF: 8-3 Trigonometry triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 3 Using Inverses KEY: inverse of cosine and sine angle measure using sine and cosine cosine 21. ANS: 35 PTS: 1 DIF: L3 REF: 8-3 Trigonometry triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 3 Using Inverses KEY: inverse of cosine and sine angle measure using sine and cosine sine 22. ANS: 60 PTS: 1 DIF: L2 REF: 8-3 Trigonometry triangles STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-3 Problem 3 Using Inverses KEY: inverse of tangent tangent tangent ratio angle measure using tangent 4

14 23. ANS: 1.4 mi PTS: 1 DIF: L3 REF: 8-4 Angles of Elevation and Depression OBJ: Use angles of elevation and depression to solve problems STA: MA.912.G.5.4 MA.912.T.2.1 TOP: 8-4 Problem 3 Using the Angle of Depression KEY: side length using sine and cosine word problem problem solving sine angles of elevation and depression sine ratio 24. ANS: 60 ; 60 PTS: 1 DIF: L4 REF: 10-3 Areas of Regular Polygons OBJ: Find the area of a regular polygon STA: MA.912.G.2.5 MA.912.G.2.7 MA.912.G.5.3 MA.912.G.6.1 TOP: 10-3 Problem 1 Finding Angle Measures KEY: regular polygon multi-part question hexagon radius 25. ANS: 3.7 in. PTS: 1 DIF: L4 REF: 10-3 Areas of Regular Polygons OBJ: Find the area of a regular polygon STA: MA.912.G.2.5 MA.912.G.2.7 MA.912.G.5.3 MA.912.G.6.1 TOP: 10-3 Problem 2 Finding the Area of a Regular Polygon KEY: regular polygon hexagon area apothem radius 26. ANS: cm 2 PTS: 1 DIF: L3 REF: 10-3 Areas of Regular Polygons OBJ: Find the area of a regular polygon STA: MA.912.G.2.5 MA.912.G.2.7 MA.912.G.5.3 MA.912.G.6.1 TOP: 10-3 Problem 3 Using Special Triangles to Find Area KEY: regular polygon hexagon area apothem radius word problem problem solving 27. ANS: m 2 PTS: 1 DIF: L2 REF: 10-3 Areas of Regular Polygons OBJ: Find the area of a regular polygon STA: MA.912.G.2.5 MA.912.G.2.7 MA.912.G.5.3 MA.912.G.6.1 TOP: 10-3 Problem 3 Using Special Triangles to Find Area KEY: regular polygon hexagon area apothem radius 5

15 28. ANS: 172 cm 2 PTS: 1 DIF: L3 REF: 10-5 Trigonometry and Area OBJ: Find areas of regular polygons and triangles using trigonometry STA: MA.912.G.2.5 MA.912.T.2.1 TOP: 10-5 Problem 1 Finding Area KEY: area of a regular polygon area regular polygon tangent measure of central angle of a regular polygon 29. ANS: 63.4 cm 2 PTS: 1 DIF: L2 REF: 10-5 Trigonometry and Area OBJ: Find areas of regular polygons and triangles using trigonometry STA: MA.912.G.2.5 MA.912.T.2.1 TOP: 10-5 Problem 3 Finding Area KEY: area of a triangle area sine 30. ANS: 40 PTS: 1 DIF: L3 REF: 11-1 Space Figures and Cross Sections OBJ: Recognize polyhedra and their parts STA: MA.912.G.7.2 MA.912.G.7.3 TOP: 11-1 Problem 2 Using Euler's Formula KEY: polyhedron face vertices edge Euler's Formula DOK: DOK ANS: 20 edges PTS: 1 DIF: L4 REF: 11-1 Space Figures and Cross Sections OBJ: Recognize polyhedra and their parts STA: MA.912.G.7.2 MA.912.G.7.3 TOP: 11-1 Problem 2 Using Euler's Formula KEY: edge Euler's Formula face polyhedron problem solving word problem vertices 32. ANS: 322 m 2 ; 332 m 2 PTS: 1 DIF: L4 REF: 11-2 Surface Areas of Prisms and Cylinders OBJ: Find the surface area of a prism and a cylinder STA: MA.912.G.7.1 MA.912.G.7.5 MA.912.G.7.7 TOP: 11-2 Problem 2 Using Formulas to Find Surface Area of a Prism KEY: surface area formulas lateral area surface area prism surface area of a prism 6

16 33. ANS: 3204 in. 2 PTS: 1 DIF: L4 REF: 11-2 Surface Areas of Prisms and Cylinders OBJ: Find the surface area of a prism and a cylinder STA: MA.912.G.7.1 MA.912.G.7.5 MA.912.G.7.7 TOP: 11-2 Problem 3 Finding Surface Area of a Cylinder KEY: surface area of a cylinder cylinder surface area formulas surface area 34. ANS: 5616 in. 2 PTS: 1 DIF: L3 REF: 11-2 Surface Areas of Prisms and Cylinders OBJ: Find the surface area of a prism and a cylinder STA: MA.912.G.7.1 MA.912.G.7.5 MA.912.G.7.7 TOP: 11-2 Problem 3 Finding Surface Area of a Cylinder KEY: cylinder surface area of a cylinder surface area formulas surface area word problem 35. ANS: 95 ft 2 PTS: 1 DIF: L3 REF: 11-3 Surface Areas of Pyramids and Cones OBJ: Find the surface area of a pyramid and a cone STA: MA.912.G.7.5 MA.912.G.7.7 TOP: 11-3 Problem 1 Finding the Surface Area of a Pyramid KEY: surface area of a pyramid surface area surface area formulas pyramid 36. ANS: 6.2 mm PTS: 1 DIF: L2 REF: 11-3 Surface Areas of Pyramids and Cones OBJ: Find the surface area of a pyramid and a cone STA: MA.912.G.7.5 MA.912.G.7.7 TOP: 11-3 Problem 2 Finding the Lateral Area of a Pyramid KEY: pyramid slant height of a pyramid Pythagorean Theorem 37. ANS: 60 cm 2 PTS: 1 DIF: L3 REF: 11-3 Surface Areas of Pyramids and Cones OBJ: Find the surface area of a pyramid and a cone STA: MA.912.G.7.5 MA.912.G.7.7 TOP: 11-3 Problem 3 Finding the Surface Area of a Cone KEY: surface area of a cone surface area formulas surface area cone 7

17 38. ANS: 18 cm PTS: 1 DIF: L2 REF: 11-3 Surface Areas of Pyramids and Cones OBJ: Find the surface area of a pyramid and a cone STA: MA.912.G.7.5 MA.912.G.7.7 TOP: 11-3 Problem 4 Finding the Lateral Area of a Cone KEY: cone lateral area slant height of a cone 39. ANS: yd 3 PTS: 1 DIF: L3 REF: 11-4 Volumes of Prisms and Cylinders OBJ: Find the volume of a prism and the volume of a cylinder STA: MA.912.G.7.5 MA.912.G.7.7 TOP: 11-4 Problem 2 Finding the Volume of a Triangular Prism KEY: volume of a triangular prism volume formulas volume prism 40. ANS: $ PTS: 1 DIF: L4 REF: 11-4 Volumes of Prisms and Cylinders OBJ: Find the volume of a prism and the volume of a cylinder STA: MA.912.G.7.5 MA.912.G.7.7 TOP: 11-4 Problem 1 Finding the Volume of a Rectangular Prism KEY: volume of a rectangular prism prism problem solving word problem volume formulas volume 41. ANS: m 3 PTS: 1 DIF: L3 REF: 11-4 Volumes of Prisms and Cylinders OBJ: Find the volume of a prism and the volume of a cylinder STA: MA.912.G.7.5 MA.912.G.7.7 TOP: 11-4 Problem 3 Finding the Volume of a Cylinder KEY: volume of a cylinder cylinder volume formulas volume 42. ANS: 944 mm 3 PTS: 1 DIF: L4 REF: 11-4 Volumes of Prisms and Cylinders OBJ: Find the volume of a prism and the volume of a cylinder STA: MA.912.G.7.5 MA.912.G.7.7 TOP: 11-4 Problem 4 Finding Volume of a Composite Figure KEY: volume of a composite figure cylinder volume of a cylinder composite space figure volume of a rectangular prism volume formulas volume prism 8

18 43. ANS: 605 cm 3 PTS: 1 DIF: L2 REF: 11-5 Volumes of Pyramids and Cones OBJ: Find the volume of a pyramid and of a cone STA: MA.912.G.7.5 MA.912.G.7.7 TOP: 11-5 Problem 1 Finding Volume of a Pyramid KEY: volume of a pyramid pyramid volume formulas volume 44. ANS: m 3 PTS: 1 DIF: L3 REF: 11-5 Volumes of Pyramids and Cones OBJ: Find the volume of a pyramid and of a cone STA: MA.912.G.7.5 MA.912.G.7.7 TOP: 11-5 Problem 3 Finding the Volume of a Cone KEY: volume of a cone volume formulas volume cone 45. ANS: 39 cm 2 PTS: 1 DIF: L3 REF: 11-6 Surface Areas and Volumes of Spheres OBJ: Find the surface area and volume of a sphere STA: MA.912.G.7.4 MA.912.G.7.5 MA.912.G.7.7 TOP: 11-6 Problem 2 Finding Surface Area KEY: circumference of a circle surface area of a sphere surface area surface area formulas sphere 46. ANS: 3054 mm 3 PTS: 1 DIF: L2 REF: 11-6 Surface Areas and Volumes of Spheres OBJ: Find the surface area and volume of a sphere STA: MA.912.G.7.4 MA.912.G.7.5 MA.912.G.7.7 TOP: 11-6 Problem 3 Finding the Volume of a Sphere KEY: volume of a sphere sphere volume formulas volume 47. ANS: m 2 PTS: 1 DIF: L3 REF: 11-6 Surface Areas and Volumes of Spheres OBJ: Find the surface area and volume of a sphere STA: MA.912.G.7.4 MA.912.G.7.5 MA.912.G.7.7 TOP: 11-6 Problem 4 Using Volume to Find Surface Area KEY: surface area of a sphere problem solving word problem sphere surface area surface area formulas volume 9

19 48. ANS: yes; 1 : 3 PTS: 1 DIF: L3 REF: 11-7 Areas and Volumes of Similar Solids OBJ: Compare and find the areas and volumes of similar solids STA: MA.912.G.7.6 TOP: 11-7 Problem 1 Identifying Similar Solids KEY: similar solids similarity ratio rectangular prism 49. ANS: 3 : 5 PTS: 1 DIF: L3 REF: 11-7 Areas and Volumes of Similar Solids OBJ: Compare and find the areas and volumes of similar solids STA: MA.912.G.7.6 TOP: 11-7 Problem 2 Finding the Scale Factor KEY: similarity ratio volumes of similar solids 50. ANS: 393 yd 3 PTS: 1 DIF: L3 REF: 11-7 Areas and Volumes of Similar Solids OBJ: Compare and find the areas and volumes of similar solids STA: MA.912.G.7.6 TOP: 11-7 Problem 3 Using a Scale Factor KEY: similarity ratio ratio of surface areas of similar solids ratio of volumes of similar solids 10