PLC Papers Created For: Year 10 Topic Practice Papers: Polygons
Polygons 1 Grade 4 Look at the shapes below A B C Shape A, B and C are polygons Write down the mathematical name for each of the polygons A. (1) B. (1) C. (1) Question 2. (Total 3 marks) (a) What is the mathematical name for a12-sided polygon? (b) What is the mathematical name for a regular quadrilateral? (1) (1)
Question 3. This diagram shows a tessellation of regular hexagons. Explain how to use the diagram to calculate the interior angle of a regular hexagon Question 4 This diagram shows a regular octagon drawn inside a circle. Use the diagram to calculate the interior angle of a regular octagon (Total 3 marks)
Polygons 2 Grade 4 Look at the shapes below A B D F G J C E H a) Which shapes are regular?.. (3) b) Which shapes are hexagons?.. (2) c) Which shape is not a polygon?.. (1) Question 2. Draw a nonagon. (Total 6 marks)
Question 3. This diagram shows a tessellation of regular hexagons. Explain how to use the diagram to calculate the interior angle of a regular octagon
Polygons 3 Grade 4 The grid below shows 5 shapes that can be fitted together to make more shapes. You can fit the shapes together to make polygons with 5, 6, 7, 8, 9 and 10 sides. Show how you can use the shapes to make 5 different polygons and draw them on the grid. You do not have to use all the shapes for each polygon but each polygon should have a different number of sides.
Polygons 4 Grade 4 The diagram below shows a pentagon with the diagonals drawn from one vertex to the other vertices. a) Use the diagram to calculate the sum of the interior angles of a pentagon. b) Draw similar diagrams to help you complete the table below. (2) Number of sides Name of polygon Sum of interior angles 5 6 7 8 (8)
PLC Papers Created For: Year 10 Topic Practice Papers: Polygons
Polygons 1 Grade 4 Solutions Look at the shapes below A B C Shape A, B and C are polygons Write down the mathematical name for each of the polygons A Hexagon 1M (1) B Pentagon 1M (1) C Decagon 1M (1) Question 2. (Total 3 marks) (a) What is the mathematical name for a12-sided polygon? (b) What is the mathematical name for a regular quadrilateral? Dodecagon 1M (1) Square 1M (1)
Question 3. This diagram shows a tessellation of regular hexagons. Explain how to use the diagram to calculate the interior angle of a regular hexagon 3 hexagons meet at each corner 1M 360 3 = 120 The interior angle is 120 0 1M Question 4 This diagram shows a regular octagon drawn inside a circle. Use the diagram to calculate the interior angle of a regular octagon 360 8 = 45 1M 180 45 = 135 and 135 2 = 67.2 1M 67.5 + 67.5 = 135 The interior angle is 135 0 1M 67.5 45 67.5 67.5 (Total 3 marks)
Polygons 2 Grade 4 Solutions Look at the shapes below A B D F G J C E H a) Which shapes are regular? A, E and J 1 mark each, no extras (3) b) Which shapes are hexagons? B and F 1 mark each, no extras (2) c) Which shape is not a polygon? D 1 mark (1) (Total 6 marks) Question 2. Draw a nonagon. 1M shape with straight sides 1M shape with 9 sides
Question 3. This diagram shows a tessellation of regular hexagons. Explain how to use the diagram to calculate the interior angle of a regular octagon 360 90 = 270 1M 270 2 = 135 The interior angle is 135 0 1M
Polygons 3 Grade 4 Solutions The grid below shows 5 shapes that can be fitted together to make more shapes. You can fit the shapes together to make polygons with 5, 6, 7, 8, 9 and 10 sides. Show how you can use the shapes to make 5 different polygons and draw them on the grid. You do not have to use all the shapes for each polygon but each polygon should have a different number of sides. 5 7 9 5 Examples of polygons shown on the grid. 6 8 10 1 mark for each polygon drawn 1 mark if given shapes are used to make it
Polygons 4 Grade 4 Solutions The diagram below shows a pentagon with the diagonals drawn from one vertex to the other vertices. a) Use the diagram to calculate the sum of the interior angles of a pentagon. 3 triangles so 3 180 = 540 0 1M calculation 1M correct total b) Draw similar diagrams to help you complete the table below. You must explain how you found the sum of the interior angles. (2) Number of sides Name of polygon Sum of interior angles 5 Pentagon 540 6 Hexagon 720 7 Heptagon 900 8 Octagon 1080 9 Nonagon 1260 2 marks for all names correct (1M if 2 names are correct but not for pentagon) 4 marks for correct sum of interior angles (1M for each correct value) 2 marks for diagrams or calculations showing method for 2 different polygons (8)