GCSE Maths Revision | Geometry and Measure

2D Shapes - Worksheet

Skill
Group A - Perimeter of 2D shapes
Work out the perimeter of the shapes. Give your answers to 1 decimal place where necessary.
1) 2) 3)

4) 5) 6)

7) 8) 9)

10) 11) 12)

© Third Space Learning 2021. You may photocopy this page.

1
 GCSE Maths Revision | Geometry and Measure

2D Shapes - Worksheet

Group B - Area of 2D shapes

Work out the area of the shapes. Give your answers to 1 decimal place where necessary and
be careful with units.
1) 2) 3)

4) 5) 6)

7) 8) 9)

10) 11) 12)

thirdspacelearning.com Helping schools close the maths attainment gap through targeted one to one teaching and flexible resources
2
GCSE Maths Revision | Geometry and Measure

2D Shapes - Worksheet

Group C - Angles in polygons

Find the required angle or value:
1) Find the size of 𝑥. 2) Find the size of 𝑥. 3) Find the size of 𝑥.

4) The exterior angle of a 5) The interior angle of a 6) The sum of the interior
regular nonagon. regular decagon. angles of a 11-sided shape.

7) A regular polygon has an 8) A regular polygon has an 9) A polygon has an interior

exterior angle of 20°. Find the interior angle of 168°. Find the angle sum of 2340°. Find the
number of sides. number of sides. number of sides.

10) Find the size of 𝑥. 11) Find the size of 𝑥. 12) Find the size of 𝑥.

© Third Space Learning 2021. You may photocopy this page.

3
 GCSE Maths Revision | Geometry and Measure

2D Shapes - Worksheet

Applied

1)

(a) 𝐴, 𝐵 and 𝐷 are three vertices of a quadrilateral with one line of symmetry.
Which point is the fourth vertex?

(b) 𝐴, 𝐵 and 𝐶 are three vertices of a quadrilateral with no lines of symmetry but
rotational symmetry order 2.
Which point is the fourth vertex?

thirdspacelearning.com Helping schools close the maths attainment gap through targeted one to one teaching and flexible resources
4
GCSE Maths Revision | Geometry and Measure

2D Shapes - Worksheet

2) A farmer wants to replace the fencing around the field shown in the diagram
below.
Stock fencing is sold in rolls of 100𝑚, each costing £150.
How much will it cost the farmer to buy enough stock fencing for his field?

3) A jeweller has decided to change a previous design of an earring.

The original shape was an equilateral triangle with sides 3𝑐𝑚.

The jeweller plans to bend one side of the triangle to create a sector with radius
3𝑐𝑚 and arc length 3𝑐𝑚.

(a) Find the angle 𝑥° of the sector. Give your answer to 3 significant figures.

(b) Calculate the difference in the areas of the two shapes.

© Third Space Learning 2021. You may photocopy this page.

5
 GCSE Maths Revision | Geometry and Measure

2D Shapes - Worksheet

4) A graphic designer is creating a new logo.

The logo is made from regular polygons.

(a) Find the size of angle 𝑥.

(b) Find the size of angle 𝑦.

5) The diagram shows the graph of the circle with equation 𝑥 + 𝑦 = 25

2 2

(a) State the coordinates of points A and B.

(b) If 1 unit on the axes represents 1 cm, find the area and circumference of the
circle in terms of π.

thirdspacelearning.com Helping schools close the maths attainment gap through targeted one to one teaching and flexible resources
6
GCSE Maths Revision | Geometry and Measure

2D Shapes - Exam Questions

1) The hexagon 𝐴𝐵𝐶𝐷𝐸𝐹 has one line of symmetry.

Angle 𝐹𝐴𝐵= angle 𝐴𝐵𝐶 = 110°

Angle 𝐴𝐹𝐸= angle 𝐵𝐶𝐷.
Angle 𝐹𝐸𝐷= angle 𝐶𝐷𝐸.
Angle 𝐶𝐷𝐸: angle 𝐵𝐶𝐷 = 3 : 2.

Find the size of angle 𝐴𝐹𝐸.

….…………… °
(5 marks)

2) The perimeter of the rectangle is twice the perimeter of the

isosceles triangle. Measurements are in cm.

Find the area of the rectangle.

….………cm2
(5 marks)

© Third Space Learning 2021. You may photocopy this page.

7
 GCSE Maths Revision | Geometry and Measure

2D Shapes - Exam Questions

3) The sector has a perimeter 25𝑐𝑚 and radius 6𝑐𝑚.

Find the size of angle 𝑥. Give your answer to 3 significant

figures.
….……………
(3 marks)

4) A regular polygon has interior angles and exterior angles in

the ratio 13 : 2.
Find the number of sides.

….……………
(3 marks)

thirdspacelearning.com Helping schools close the maths attainment gap through targeted one to one teaching and flexible resources
8
GCSE Maths Revision | Geometry and Measure

2D Shapes - Answers

Question Answer

Skill Questions

Group A Work out the perimeter of the shapes:

1) 1) 20𝑐𝑚

2) 2) 22𝑐𝑚

3) 3) 22𝑐𝑚

4) 4) 28𝑐𝑚

5) 5) 42𝑐𝑚

6) 6) 12𝑐𝑚

© Third Space Learning 2021. You may photocopy this page.

9
 GCSE Maths Revision | Geometry and Measure

2D Shapes - Answers

Group A 7) 7) 6π 𝑐𝑚 𝑜𝑟 18. 8 𝑐𝑚 (1 d.p.)

contd

8) 8) 9π 𝑐𝑚 𝑜𝑟 28. 3 𝑐𝑚 (1 d.p.)

9) 9) 28. 6 𝑐𝑚 (1 d.p.)

10) 10) 55. 7 𝑐𝑚 (1 d.p.)

11) 11) 36. 6 𝑐𝑚 (1 d.p.)

12) 12) 25. 5𝑐𝑚 (1 d.p.)

thirdspacelearning.com Helping schools close the maths attainment gap through targeted one to one teaching and flexible resources
10
GCSE Maths Revision | Geometry and Measure

2D Shapes - Answers

Group B Work out the area of the shapes:

2
1) 1) 40𝑐𝑚

2
2) 2) 9. 43𝑐𝑚

2
3) 3) 63𝑐𝑚

2
4) 4) 24𝑐𝑚

2
5) 5) 16. 5𝑐𝑚

2
6) 6) 135𝑐𝑚

2
7) 7) 250𝑐𝑚

© Third Space Learning 2021. You may photocopy this page.

11
 GCSE Maths Revision | Geometry and Measure

2D Shapes - Answers

2 2
Group B 8) 8) 64π 𝑐𝑚 or 201. 1 𝑐𝑚 (1 d.p.)
contd

2 2
9) 9) 121π 𝑐𝑚 or 380. 1 𝑐𝑚 (1 d.p.)

2
10) 10) 43. 6𝑐𝑚 (1 d.p.)

2
11) 11) 18. 3𝑐𝑚 (1 d.p.)

2
12) 12) 71. 8𝑐𝑚 (1 d.p.)

thirdspacelearning.com Helping schools close the maths attainment gap through targeted one to one teaching and flexible resources
12
GCSE Maths Revision | Geometry and Measure

2D Shapes - Answers

Group C Find the required angle or value:

1) Find the size of 𝑥. 1) 120°

2) Find the size of 𝑥. 2) 72°

3) Find the size of 𝑥. 3) 135°

4) The exterior angle of a regular nonagon. 4) 40°

5) The interior angle of a regular decagon. 5) 144°

6) The sum of the interior angles of a 11-sided 6) 1620°

shape.

7) A regular polygon has an exterior angle of 7) 18

20°. Find the number of sides.

8) A regular polygon has an interior angle of 8) 30

168°. Find the number of sides.

9) A polygon has an interior angle sum of 9) 15

2340°. Find the number of sides.

© Third Space Learning 2021. You may photocopy this page.

13
 GCSE Maths Revision | Geometry and Measure

2D Shapes - Answers

Group C 10) Find the size of 𝑥. 10) 113°

contd

11) Find the size of 𝑥. 11) 150°

12) Find the size of 𝑥. 12) 42°

thirdspacelearning.com Helping schools close the maths attainment gap through targeted one to one teaching and flexible resources
14
GCSE Maths Revision | Geometry and Measure

2D Shapes - Answers

Question Answer

Applied Questions

1)

a) 𝐴, 𝐵 and 𝐷 are three vertices of a quadrilateral a) 𝐹

with one line of symmetry.
What point is the fourth vertex?
b) 𝐴, 𝐵 and 𝐶 are three vertices of a quadrilateral b) 𝐹
with no lines of symmetry but rotational
symmetry order 2.
What point is the fourth vertex?

2) A farmer wants to replace the fencing around Perimeter = 550𝑚

the field shown in the diagram below. Cost = £900
Stock fencing is sold in rolls of 100𝑚, each
costing £150.
How much will it cost the farmer to buy enough
stock fencing for his field?

© Third Space Learning 2021. You may photocopy this page.

15
 GCSE Maths Revision | Geometry and Measure

2D Shapes - Answers

3) A jeweller has decided to change a previous

design of an earring.

The original shape was an equilateral

triangle with sides 3𝑐𝑚.
The jeweller plans to bend one side of the
triangle to create a sector with radius 3𝑐𝑚
and arc length 3𝑐𝑚.

a) Find the angle 𝑥° of the sector. a) 57. 3° (1 d.p.)

b) Calculate the difference in the areas of the b) Triangle = 3. 89711…𝑐𝑚2

two shapes. 2
Sector = 4. 5𝑐𝑚
2
Difference = 0. 60𝑐𝑚

4) A graphic designer is creating a new logo.

The logo consists of regular polygons.

a) Find 𝑥 a) 90°

b) Find 𝑦 b) 15°

thirdspacelearning.com Helping schools close the maths attainment gap through targeted one to one teaching and flexible resources
16
GCSE Maths Revision | Geometry and Measure

2D Shapes - Answers

5) The diagram shows the graph of the circle

2 2
with equation 𝑥 + 𝑦 = 25

a) State the coordinates of points A and B. a) A = (0, 5)

B = (5, 0)
b) If 1 unit on the axes represents 1 cm, find the b) Area = 25π𝑐𝑚
2

area and circumference of the circle in terms

Circumference = 10π𝑐𝑚
of π.

© Third Space Learning 2021. You may photocopy this page.

17
GCSE Maths Revision | Geometry and Measure

2D Shapes - Mark Scheme

Question Answer

Exam Questions

1) The hexagon ABCDEF has one line of Indicating sum of angles is 720° or 540° if
symmetry. line of symmetry used to form a pentagon (1)

720 − (110 + 110) = 500 or

540 − (110 + 180) = 250 (1)

Use of ratio 3: 2
or 3𝑥 and 2𝑥 seen
or 5𝑥 = 250 (1)

Angle 𝐹𝐴𝐵 = angle 𝐴𝐵𝐶 = 110°

𝑥 = 50 (1)
Angle 𝐴𝐹𝐸 = angle 𝐵𝐶𝐷.
Angle 𝐴𝐹𝐸 = 100° (1)
Angle 𝐹𝐸𝐷 = angle 𝐶𝐷𝐸.
Angle 𝐶𝐷𝐸: angle 𝐵𝐶𝐷 = 3 : 2.

Find the size of angle 𝐴𝐹𝐸.

2) The perimeter of the rectangle is twice 6𝑥 + 2 or 2𝑥 + 5 seen (1)

the perimeter of the isosceles triangle.
Measurements are in cm. 6𝑥 + 2 = 2(2𝑥 + 5) oe (1)

𝑥=4 (1)

2𝑥 − 1 = 2(4) − 1 = 7 and
𝑥 + 2 = (4) + 2 = 6 (1)

Find the area of the rectangle. (6 × 7) = 42 𝑐𝑚

2
(1)
3) The sector has a perimeter 25𝑐𝑚 and Sight of arc length given as 13𝑐𝑚 (1)
radius 6𝑐𝑚.
𝑥
360
× 2 × π × 6 = 13 oe (1)

𝑥 = 124° (1)

Find the size of angle 𝑥. Give your

answer to 3 significant figures.
GCSE Maths Revision | Geometry and Measure

2D Shapes - Mark Scheme

4) A regular polygon has interior angles 180 ÷ 5 = 24 oe (1)

and exterior angles in the ratio 13 : 2
Find the number of sides. 156° or 24° seen (1)

15 sides (1)

Do you have KS4 students who need additional support in maths?

Our specialist tutors will help them develop the skills they need to succeed at GCSE in weekly one to one online
revision lessons. Trusted by secondary schools across the UK.

Visit thirdspacelearning.com to find out more.