Year 8 Shape and Geometry Worksheet - Intermediate

Year 8 Shape and Geometry worksheet for Year 8 (Key Stage 3 / Year 7-9 (Ages 11-14)). Intermediate level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.

Maths•Key Stage 3 / Year 7-9 (Ages 11-14)•Geometryintermediate

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Year 8 Shape and Geometry: Angles, Circles and 3D Measures

Key Stage 3 • Ages 12–13 • Intermediate

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Instructions: Show your working clearly and include units where needed. Use π = 3.14 unless a question asks for an answer in terms of π. Check whether your answer should be in degrees, linear units, square units or cubic units.

Angles in Parallel Lines

Use the angle relationships for parallel lines cut by a transversal. Alternate angles and corresponding angles are equal; co-interior angles sum to 180°. Find each unknown angle and show your working.

1. A pair of alternate angles are (3x + 10)° and 70°. Find x. [2 marks]

2. A pair of corresponding angles are (2y + 15)° and 95°. Find y. [2 marks]

3. A pair of co-interior angles are 3z° and 120°. Find z. [2 marks]

4. A pair of co-interior angles are (x + 25)° and (2x + 5)°. Find x. [3 marks]

Interior and Exterior Polygon Angles

Use the sum of the interior angles of an n-sided polygon, (n − 2) × 180°. For a regular polygon, all exterior angles are equal and their sum is 360°. Give angle answers in degrees.

1. Find the sum of the interior angles of a hexagon. [2 marks]

2. Find each interior angle of a regular octagon. [2 marks]

3. A regular polygon has an exterior angle of 45°. How many sides does it have? [2 marks]

4. A regular polygon has 12 sides. Find each exterior angle and each interior angle. [3 marks]

Circumference and Area of Circles

Use C = 2πr for circumference and A = πr² for area. Use π = 3.14 and round decimal answers to 1 decimal place where necessary. Include the correct units.

1. A circle has radius 5 cm. Calculate its circumference. [2 marks]

2. A circle has diameter 12 m. Calculate its circumference. [2 marks]

3. A circle has radius 4 cm. Calculate its area. [2 marks]

4. A circular pond has diameter 10 m. Calculate its area. [2 marks]

Volume of Cuboids and Prisms

For a cuboid, use volume = length × width × height. For a prism, use volume = cross-sectional area × length. Write your answers in cubic units.

1. Find the volume of a cuboid measuring 8 cm by 3 cm by 5 cm. [2 marks]

2. A cuboid has a base measuring 6 m by 4 m and a height of 2.5 m. Find its volume. [2 marks]

3. A triangular prism has a right-angled triangular cross-section with perpendicular sides 3 cm and 4 cm. The prism is 10 cm long. Find its volume. [3 marks]

4. A prism has a cross-sectional area of 18 cm² and a length of 7 cm. Find its volume. [2 marks]

Surface Area of Cuboids and Prisms

For a cuboid, add the areas of all six faces, or use 2(lw + lh + wh). For a prism, add the areas of its two end faces and its rectangular side faces. Give your answers in square units.

1. Find the surface area of a cuboid measuring 5 cm by 3 cm by 2 cm. [3 marks]

2. Find the surface area of a cuboid measuring 8 m by 4 m by 3 m. [3 marks]

3. A triangular prism has a right-angled triangular end with sides 3 cm, 4 cm and 5 cm. Its length is 10 cm. Find its total surface area. [3 marks]

4. A prism has a cross-sectional area of 12 cm² and a cross-sectional perimeter of 16 cm. Its length is 5 cm. Find its total surface area. [3 marks]

Answer Key

Activity 1: 20 ; 40 ; 20 ; 50

Activity 2: 720° ; 135° ; 8 sides ; exterior angle 30°, interior angle 150°

Activity 3: 31.4 cm ; 37.68 m ; 50.24 cm² ; 78.5 m²

Activity 4: 120 cm³ ; 60 m³ ; 60 cm³ ; 126 cm³

Activity 5: 62 cm² ; 136 m² ; 132 cm² ; 104 cm²