Polygons: Edexcel International GCSE Maths questions

Every Edexcel International GCSE Maths exam question on 4.2 Polygons, 2019–2025, with its mark scheme and examiner’s report.

All 97 questions on Polygons, as a list

June 2025 (R), Paper 1 Foundation, Q3 (4 marks): The diagram shows a 6-sided polygon. x B A (a) Measure the length of the side AB Give the units of your answer. (b) Measure the size of the angle marked x ° (c)
June 2025 (R), Paper 1 Foundation, Q7 (5 marks): A D Diagram NOT E accurately drawn x° 58° B C AEC and BED are straight lines. Sergio says that the value of x is 58 (a) Give a reason why Sergio is correct. In
June 2025 (R), Paper 2 Foundation, Q3 (4 marks): Here is a 3-D shape. (a) (i) Write down the mathematical name of this shape. (ii) Write down the number of edges of this shape. Here are six quadrilaterals on a
June 2025, Paper 1 Foundation, Q20 (4 marks): Diagram NOT accurately drawn C 50° B 148° A AB and BC are two sides of a regular polygon with n sides. Work out the value of n Show your working clearly. n =
June 2025, Paper 1 Higher, Q3 (4 marks): Diagram NOT accurately drawn C 50 B 148 A AB and BC are two sides of a regular polygon with n sides. Work out the value of n Show your working clearly. n =
November 2024, Paper 1 Foundation, Q2 (4 marks): Here are two shapes. Quadrilateral Triangle (a) Write down the mathematical name of the (i) triangle, (ii) quadrilateral. (b) On the triangle, draw the line of
November 2024, Paper 1 Foundation, Q7 (4 marks): B C 125° 107° Diagram NOT accurately drawn x° A 138° D E ABCD is a quadrilateral. ADE is a straight line. Work out the value of x Give a reason for each stage o
November 2024, Paper 2 Foundation, Q27 (5 marks): C Diagram NOT I accurately drawn D B H E A G F ABCDE is a regular pentagon. DEFGHI is a regular hexagon. AF is a straight line. Work out the size of angle EAF °
November 2024, Paper 2 Higher, Q11 (5 marks): C Diagram NOT I accurately drawn D B H E A G F ABCDE is a regular pentagon. DEFGHI is a regular hexagon. AF is a straight line. Work out the size of angle EAF °
June 2024 (R), Paper 1 Foundation, Q6 (4 marks): The diagram shows a regular octagon. (a) Write down the number of lines of symmetry of a regular octagon. Here is a shape. x (b) On the shape, mark with a let
June 2024 (R), Paper 1 Foundation, Q12 (5 marks): B Diagram NOT C accurately drawn 128° A 78° 86° 125° D E F ABCD is a quadrilateral. CDE is an isosceles triangle with CD = CE DEF is a straight line. Work out t
June 2024 (R), Paper 2 Foundation, Q4 (3 marks): Here is a quadrilateral. (a) What is the mathematical name for this type of quadrilateral? The diagram shows a 3-D shape. (b) (i) What is the mathematical nam
June 2024 (R), Paper 2 Foundation, Q12 (2 marks): The size of each exterior angle of a regular polygon is 15° Work out the number of sides of the regular polygon.
June 2024 (R), Paper 2 Higher, Q15 (3 marks): A D Diagram NOT accurately drawn 6.5 cm B C E 3 cm AB, BC and CD are three sides of a regular pentagon and CDE is a triangle. BCE is a straight line. CD = 6.5 c
June 2024, Paper 1 Foundation, Q4 (4 marks): Here is a polygon. (a) Write down the mathematical name of this polygon. (b) Write down the number marked with the arrow. 100 200 300 400 Here are four clock fa
June 2024, Paper 1 Foundation, Q6 (5 marks): 235° Diagram NOT x° accurately drawn (a) (i) Work out the value of x x = (ii) Give a reason for your answer. D Diagram NOT E y° accurately drawn 98° 54° A B C A
June 2024, Paper 1 Foundation, Q20 (4 marks): In the diagram, ABCDE is a regular pentagon. F 96° E A Diagram NOT accurately drawn D B C Angle AEF = 96° Work out the size of the obtuse angle FED Show your wo
June 2024, Paper 1 Higher, Q5 (4 marks): In the diagram, ABCDE is a regular pentagon. F 96° E A Diagram NOT accurately drawn D B C Angle AEF = 96° Work out the size of the obtuse angle FED Show your wo
June 2024, Paper 1 Higher, Q24 (6 marks): A polygon has n sides, where n > 5 The interior angles of the polygon form an arithmetic sequence. The smallest angle of the polygon is 84° The common differenc
November 2023, Paper 1 Foundation, Q3 (4 marks): (a) x Write down the mathematical name of the angle marked x P O P is a point on a circle with centre O (b) Write down the mathematical name of the line OP Here
November 2023, Paper 1 Foundation, Q4 (5 marks): The diagram shows three points, A, B and C, marked on a grid. y 7 A 6 5 4 3 2 1 O x −5 −4 −3 −2 −1 1 2 3 4 5 6 7 −1 B −2 C −3 (a) Write down the coordinates of
June 2023 (R), Paper 1 Foundation, Q3 (3 marks): The diagram shows a 5-sided polygon, ABCDE D E C A B (a) Write down the mathematical name for a 5-sided polygon. (b) Measure the length of the line AB Give your
June 2023 (R), Paper 1 Foundation, Q10 (5 marks): The diagram shows quadrilateral ABCD E Diagram NOT accurately drawn 108° F C B 135° x° 54° G D A ECD, BCF and GAD are straight lines. Work out the value of x Gi
June 2023 (R), Paper 1 Higher, Q15 (4 marks): D A Diagram NOT accurately drawn 57° C B 104° E 95° 149° G F BCDEFG is a hexagon. AB, BC and CD are three sides of a regular n‑sided polygon. Calculate the valu
June 2023 (R), Paper 2 Foundation, Q4 (3 marks): y 7 P 6 5 4 Q 3 2 1 O x –5 –4 –3 –2 –1 1 2 3 4 5 6 7 –1 R –2 (a) Write down the coordinates of the point (i) P ( , ) (ii) Q ( , ) (b) On the grid above, mark wi
June 2023 (R), Paper 2 Foundation, Q9 (3 marks): The diagram shows quadrilateral ABCD D Diagram NOT accurately drawn y° x° C 32° A B BC = CD = DB angle DBA = 90° and angle DAB = 32° (a) Work out the value of x
June 2023, Paper 1 Higher, Q22 (6 marks): The diagram shows two circles with centre O and a regular pentagon ABCDE B Diagram NOT accurately drawn A O C E D A, B, C, D and E are points on the larger circ
June 2023, Paper 2 Foundation, Q5 (5 marks): The diagram shows three points, A, B and C, marked on a grid. y 5 4 A 3 2 B 1 O x –1 1 2 3 4 5 6 7 –1 C –2 (a) Write down the coordinates of point A ( , ) (b) O
June 2023, Paper 2 Foundation, Q6 (3 marks): (a) Write down the mathematical name of this polygon. (b) Measure the length of the line AB Give your answer in centimetres. A B cm Here are six triangles drawn
June 2023, Paper 2 Foundation, Q27 (3 marks): Here is a 9-sided regular polygon ABCDEFGHJ, with centre O A Diagram NOT J B accurately drawn H C O D G x° F E K ODK and FEK are straight lines. Work out the va
June 2023, Paper 2 Higher, Q11 (3 marks): Here is a 9-sided regular polygon ABCDEFGHJ, with centre O A Diagram NOT J B accurately drawn H C O D G x° F E K ODK and FEK are straight lines. Work out the va
June 2023, Paper 2 Higher, Q24 (6 marks): ABCD is a kite with AB = AD and CB = CD A is the point with coordinates (–2, 10) 27 B is the point with coordinates , 4 5 C is the point with coordinates (
January 2023 (R), Paper 1 Foundation, Q9 (4 marks): E D Diagram NOT 112° accurately drawn x° 52° A B C BCD is an isosceles triangle with BD = CD ABC is a straight line. ABDE is a quadrilateral. Work out the value
January 2023 (R), Paper 2 Foundation, Q3 (4 marks): (a) Write down the mathematical name for an 8-sided polygon. x (b) What type of angle is the angle marked x? (c) On the diagram above, draw a chord of the circl
January 2023 (R), Paper 2 Foundation, Q25 (4 marks): A Diagram NOT R accurately drawn S 128° B F T C 32° D E V U AB, BC, CD, DE and EF are five sides of a regular polygon. RST, SCU and BCV are straight lines. RST
January 2023 (R), Paper 2 Higher, Q11 (4 marks): A Diagram NOT R accurately drawn S 128° B F T C 32° D E V U AB, BC, CD, DE and EF are five sides of a regular polygon. RST, SCU and BCV are straight lines. RST
January 2023 (R), Paper 2 Higher, Q25 (6 marks): ABCD is a trapezium with AB parallel to DC A is the point with coordinates (–4, 6) B is the point with coordinates (2, 3) D is the point with coordinates (–1, 8
January 2023, Paper 1 Foundation, Q19 (3 marks): The diagram shows a pentagon. 119° Diagram NOT 67° x° accurately drawn 135° Work out the value of x x =
January 2023, Paper 1 Higher, Q4 (3 marks): The diagram shows a pentagon. 119° Diagram NOT 67° x° accurately drawn 135° Work out the value of x x =
June 2022 (R), Paper 1 Foundation, Q2 (3 marks): Here is a 5‑sided polygon. (a) Write down the mathematical name for a 5‑sided polygon. (b) On the diagram, mark with a letter A an acute angle. (c) On the diagr
June 2022 (R), Paper 1 Foundation, Q12 (3 marks): The diagram below shows the trapezium PQRS S P Diagram NOT accurately drawn (3x – 24)° (102 – x)° Q R Angle PQR and angle QPS are right angles. Find the value o
June 2022 (R), Paper 2 Foundation, Q4 (3 marks): Here are two sides of a parallelogram. (a) On the grid above, complete the parallelogram. The diagram shows a 3‑D shape. (b) (i) What is the mathematical name o
June 2022 (R), Paper 2 Foundation, Q27 (5 marks): The diagram shows triangle ABP inside the regular hexagon ABCDEF D E Diagram NOT accurately drawn C F P B A AB = 5 cm BP = 2 cm Angle ABP = 90° Work out the siz
June 2022 (R), Paper 2 Higher, Q10 (5 marks): The diagram shows triangle ABP inside the regular hexagon ABCDEF D E Diagram NOT accurately drawn C F P B A AB = 5 cm BP = 2 cm Angle ABP = 90° Work out the siz
June 2022, Paper 1 Foundation, Q4 (4 marks): Here is a polygon. (a) Write down the mathematical name of this polygon. Here is a scale. 0 100 200 300 400 500 (b) On the scale, mark with an arrow (↑) the num
June 2022, Paper 1 Foundation, Q6 (5 marks): Diagram NOT accurately drawn x° 48° A C B ABC is a straight line. (a) (i) Work out the value of x x = (ii) Give a reason for your answer to (i) Question 6 conti
June 2022, Paper 1 Foundation, Q19 (4 marks): The diagram shows parts of three regular polygons, A, B and C, meeting at a point. B 7x° Diagram NOT C 3x° accurately drawn 8x° A Polygon B has n sides. Work ou
June 2022, Paper 1 Higher, Q4 (4 marks): The diagram shows parts of three regular polygons, A, B and C, meeting at a point. B 7x° Diagram NOT C 3x° accurately drawn 8x° A Polygon B has n sides. Work ou
June 2022, Paper 1 Higher, Q23 (6 marks): A polygon has n sides, where n > 5 When arranged in order of size, starting with the largest number, the sizes of the interior angles of the polygon, in degrees
June 2022, Paper 2 Foundation, Q2 (5 marks): Here are seven shapes on a centimetre grid. A C B D E F G (a) Write down the letters of the two shapes that are congruent. and Two of the seven shapes are simil
June 2022, Paper 2 Higher, Q22 (7 marks): ABCD is a kite, with diagonals AC and BD, drawn on a centimetre square grid, with a scale of 1 cm for 1 unit on each axis. A is the point with coordinates (−3,
January 2022 (R), Paper 1 Foundation, Q2 (3 marks): Here are three shapes. A B C Shape A is a triangle. (a) Write down the mathematical name for this type of triangle. Shape B is a rectangle. (b) On shape B, draw
January 2022 (R), Paper 2 Foundation, Q2 (5 marks): The diagram shows three points, A, B and C, on a grid. y 6 5 A 4 3 B 2 1 C O x –2 –1 1 2 3 4 5 6 7 8 9 –1 –2 (a) Write down the coordinates of (i) point A ( , )
January 2022 (R), Paper 2 Foundation, Q9 (4 marks): Here is a quadrilateral. Diagram NOT accurately drawn x° 92° x° 44° (i) Work out the value of x x = (ii) Give a reason for your answer.
January 2022 (R), Paper 2 Foundation, Q21 (4 marks): The diagram shows a regular octagon ABCDEFGH and a regular pentagon ABIJK F E G D J Diagram NOT accurately drawn K I H C x A B Work out the size of the angle x
January 2022 (R), Paper 2 Higher, Q4 (4 marks): The diagram shows a regular octagon ABCDEFGH and a regular pentagon ABIJK F E G D J Diagram NOT accurately drawn K I H C x A B Work out the size of the angle x
January 2022, Paper 1 Foundation, Q4 (5 marks): The diagram shows a 5‑sided polygon. x A B (a) Measure the length of the side AB Give the units of your answer. (b) Measure the size of the angle marked x ° (c)
January 2022, Paper 2 Foundation, Q6 (4 marks): Here are nine shapes drawn on a grid of squares. A C B F D E G H J Shape D is a quadrilateral. (a) What is the mathematical name of this quadrilateral? One of t
January 2022, Paper 2 Foundation, Q26 (4 marks): The diagram shows a regular 10-sided polygon, ABCDEFGHIJ A Diagram NOT accurately drawn J B x° y° I C H D G E F Show that x = y
January 2022, Paper 2 Higher, Q11 (4 marks): The diagram shows a regular 10-sided polygon, ABCDEFGHIJ A Diagram NOT accurately drawn J B x° y° I C H D G E F Show that x = y
November 2021, Paper 1 Foundation, Q1 (6 marks): Here are five fractions. 2 3 5 7 8 8 9 25 28 40 Two of the fractions in the table are equivalent to 1 5 (a) Put a tick () in the box underneath each of these t
November 2021, Paper 2 Foundation, Q8 (3 marks): Here is a rhombus. 122° Diagram NOT accurately drawn x° Work out the value of x. Give a reason for your answer. x =
November 2021, Paper 2 Foundation, Q21 (5 marks): The diagram shows a regular octagon ABCDHIJK and a pentagon DEFGH. E C Diagram NOT B 102° D accurately drawn 112° F 96° A H G x K I J Angle GHD = angle FGH. Wor
November 2021, Paper 2 Higher, Q5 (5 marks): The diagram shows a regular octagon ABCDHIJK and a pentagon DEFGH. E C Diagram NOT B 102° D accurately drawn 112° F 96° A H G x K I J Angle GHD = angle FGH. Wor
June 2021, Paper 1 Foundation, Q11 (3 marks): The diagram shows a square ABCD and a regular pentagon CDEFG. E Diagram NOT D accurately drawn A F C B x G Work out the size of the angle marked x. °
January 2021 (R), Paper 1 Foundation, Q3 (4 marks): Here is a quadrilateral. x (a) What is the mathematical name of this quadrilateral? (b) Measure the size of the angle marked x. ° (c) On the quadrilateral, mark
January 2021 (R), Paper 1 Foundation, Q23 (5 marks): The diagram shows a regular pentagon, ABCDE, a regular hexagon, CFGHID, and a quadrilateral, EDIJ. F B Diagram NOT accurately drawn C G A D H E I x J AEJ and HI
January 2021 (R), Paper 1 Higher, Q8 (5 marks): The diagram shows a regular pentagon, ABCDE, a regular hexagon, CFGHID, and a quadrilateral, EDIJ. F B Diagram NOT accurately drawn C G A D H E I x J AEJ and HI
January 2021, Paper 1 Foundation, Q9 (4 marks): The diagram shows quadrilateral ABCD and isosceles triangle ADE, where AE = AD. A B 59° 115° 68° C x° D E EDC is a straight line. Work out the value of x. Give
November 2020 (R), Paper 1 Foundation, Q3 (4 marks): The diagram shows five shaded shapes on a grid of squares. A B C D E Two of the shapes are congruent. (a) Write down the letters of these shapes. and (b) On the
November 2020 (R), Paper 1 Foundation, Q27 (3 marks): The diagram shows a regular octagon ABCDEFGH. H G Diagram NOT accurately drawn A F B E C D Work out the size of angle HAC. °
November 2020 (R), Paper 1 Higher, Q22 (6 marks): The diagram shows a regular octagon ABCDEFGH. B C Diagram NOT accurately drawn A D 10 cm H E G F Each side of the octagon has length 10 cm. Find the area of the
November 2020 (R), Paper 2 Foundation, Q5 (6 marks): The diagram shows a quadrilateral ABCD drawn on a square grid. A B D C (a) Measure the length of BC. cm (b) Write down the mathematical name of quadrilateral AB
November 2020 (R), Paper 2 Foundation, Q7 (4 marks): The diagram shows a trapezium ABCD in which AB and DC are parallel. A B Diagram NOT x° accurately drawn 104° 42° D C AB = DB Work out the value of x. Give a rea
November 2020, Paper 1 Foundation, Q4 (4 marks): Here is a polygon with five sides. x (a) Write down the mathematical name of a polygon with five sides. (b) Measure the size of the angle marked x. ° Two sides
November 2020, Paper 1 Foundation, Q21 (4 marks): Here is a 10-sided polygon. Diagram NOT accurately drawn 148° 150° 150° 168° 168° 134° 134° 125° 125° x° Work out the value of x. x =
November 2020, Paper 1 Higher, Q8 (4 marks): Here is a 10-sided polygon. Diagram NOT accurately drawn 148° 150° 150° 168° 168° 134° 134° 125° 125° x° Work out the value of x. x =
November 2020, Paper 2 Foundation, Q18 (5 marks): E Diagram NOT accurately drawn C F D 58° B A The diagram shows a parallelogram ABCD and an isosceles triangle DEF in which DE = DF CDF and ADE are straight line
November 2020, Paper 2 Higher, Q3 (5 marks): E Diagram NOT accurately drawn C F D 58° B A The diagram shows a parallelogram ABCD and an isosceles triangle DEF in which DE = DF CDF and ADE are straight line
January 2020 (R), Paper 1 Foundation, Q3 (4 marks): (a) On the grid below, draw a kite. (b) Write down the mathematical name of an 8-sided polygon. Here is a solid prism. (c) (i) Write down the mathematical name
January 2020 (R), Paper 1 Foundation, Q24 (5 marks): The diagram shows a regular hexagon, ABCDEF, and an isosceles triangle, GHJ. E D J Diagram NOT accurately drawn (x + 5) cm F C A B G H (x − 1) cm (2x − 3) cm Th
January 2020 (R), Paper 1 Higher, Q10 (5 marks): The diagram shows a regular hexagon, ABCDEF, and an isosceles triangle, GHJ. E D J Diagram NOT accurately drawn (x + 5) cm F C A B G H (x − 1) cm (2x − 3) cm Th
January 2020 (R), Paper 2 Foundation, Q26 (3 marks): The diagram shows two congruent isosceles triangles and parts of two congruent regular polygons, X and Y. Diagram NOT accurately drawn Polygon X A D 66° 66° B E
January 2020 (R), Paper 2 Higher, Q12 (3 marks): The diagram shows two congruent isosceles triangles and parts of two congruent regular polygons, X and Y. Diagram NOT accurately drawn Polygon X A D 66° 66° B E
January 2020, Paper 1 Foundation, Q7 (5 marks): A Diagram NOT accurately drawn 17° E 78° 125° y° x° D C B ABDE is a quadrilateral. ABC is a triangle. DCB is a straight line. (a) (i) Work out the value of x. x
January 2020, Paper 2 Foundation, Q6 (3 marks): (a) Write down the mathematical name of this 3‑D shape. 1 cm 2 cm 4 cm B (b) A Measure the length of AB. cm Here are six shapes. A B C D E F Two of these shapes
January 2020, Paper 2 Foundation, Q15 (3 marks): A regular polygon has n sides. The size of each interior angle of the regular polygon is 140° Work out the value of n. n =
June 2019 (R), Paper 1 Foundation, Q16 (3 marks): Each interior angle of a regular polygon is 162° Work out the number of sides the polygon has.
June 2019 (R), Paper 1 Higher, Q2 (3 marks): Each interior angle of a regular polygon is 162° Work out the number of sides the polygon has.
June 2019 (R), Paper 2 Foundation, Q3 (2 marks): Here is a pentagon. obtuse reflex right acute (a) Write down the word from the box that describes the angle marked x. angle (b) Write down the mathematical name
June 2019 (R), Paper 2 Foundation, Q10 (4 marks): The diagram shows kite ABCD. Diagram NOT accurately drawn D 140° (a) Work out the size of the angle marked x. The diagram shows kite PQRS. 33 cm Diagram NOT acc
June 2019, Paper 1 Foundation, Q2 (3 marks): Complete the following statements by writing a number on each dotted line. (a) A pentagon has sides. (b) The size of each angle in an equilateral triangle is °
June 2019, Paper 1 Foundation, Q13 (2 marks): Each exterior angle of a regular polygon is 24° Work out the number of sides of the polygon.
June 2019, Paper 2 Foundation, Q4 (4 marks): Here are five road signs. 35 M. P. H. B C GO D E One of these five road signs has one line of symmetry. (a) Write down the letter of this road sign. One of thes
January 2019 (R), Paper 2 Foundation, Q23 (4 marks): I H Diagram NOT accurately drawn D J G 84° E C 112° 112° F K x° A B Pentagon ABCDE is drawn inside the regular octagon ABFGHIJK. The pentagon has exactly one li
January 2019 (R), Paper 2 Higher, Q6 (4 marks): I H Diagram NOT accurately drawn D J G 84° E C 112° 112° F K x° A B Pentagon ABCDE is drawn inside the regular octagon ABFGHIJK. The pentagon has exactly one li
January 2019, Paper 2 Foundation, Q13 (5 marks): A B Diagram NOT 48° accurately drawn y 68° 243° E C D ABD is an isosceles triangle with AB = DB. DCE is a straight line. Angle ABD = 48° Angle BCE = 68° Reflex

Questions, mark schemes and examiner’s reports are © Pearson Edexcel, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? Every Edexcel International GCSE Maths paper.

Rather write your answers by hand on iPad? Plumi marks them against the same mark schemes.

2,567 questions