Year 8 Shape and Geometry Worksheet - Beginner

Year 8 Shape and Geometry worksheet for Year 8 (Key Stage 3 / Year 7-9 (Ages 11-14)). Beginner 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)•Geometrybeginner

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Year 8 Shape and Geometry: Angles, Circles and Solids

Key Stage 3 • Ages 12–13 • Beginner

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Instructions: Use the worked examples and formula reminders to help you. Show your working, include units where needed, and use π = 3.14 for circle calculations. Give each final answer in the box provided.

Angles in Parallel Lines

Use the angle facts for parallel lines: alternate angles are equal, corresponding angles are equal, and co-interior angles add to 180°. For co-interior angles, subtract the given angle from 180°. Write the missing angle in each box.

Worked example: If an alternate angle is 65°, the matching alternate angle is 65°.

1. An angle is 72°. Find the size of its alternate angle.

2. An angle is 118°. Find the size of its corresponding angle.

3. Co-interior angles are 64° and x°. Find x.

4. Co-interior angles are 137° and y°. Find y.

Interior and Exterior Angles of Polygons

For a regular polygon, each exterior angle is 360° divided by the number of sides. An interior angle and its exterior angle add to 180°. Use these facts to calculate each answer; show the calculation you used.

Worked example: A regular hexagon has exterior angle 360° ÷ 6 = 60° and interior angle 180° − 60° = 120°.

1. Find the sum of the interior angles of a pentagon.

2. Find each exterior angle of a regular octagon.

3. Find each interior angle of a regular pentagon.

4. A regular polygon has an exterior angle of 45°. How many sides does it have?

Circumference and Area of Circles

Use π = 3.14. Circumference = 2 × π × radius, or π × diameter; area = π × radius². Check whether the question gives a radius or a diameter, and include the correct units in your answer.

Worked example: A circle with radius 3 cm has circumference 2 × 3.14 × 3 = 18.84 cm.

1. A circle has radius 4 cm. Find its circumference.

2. A circle has diameter 10 cm. Find its circumference.

3. A circle has radius 5 cm. Find its area.

4. A circle has diameter 8 cm. Find its area.

Volume of Cuboids and Prisms

Volume measures the space inside a solid. For a cuboid, multiply length × width × height. For a prism, multiply the area of its cross-section by its length. Give answers in cubic units.

Worked example: A cuboid measuring 4 cm × 3 cm × 2 cm has volume 4 × 3 × 2 = 24 cm³.

1. Find the volume of a cuboid measuring 6 cm × 2 cm × 3 cm.

2. A triangular prism has a triangular cross-section with base 4 cm and perpendicular height 3 cm. Its length is 8 cm. Find its volume.

3. A cuboid has volume 60 cm³, length 5 cm and width 4 cm. Find its height.

4. A prism has a cross-sectional area of 12 cm² and length 7 cm. Find its volume.

Surface Area of Cuboids and Prisms

Surface area is the total area of all the outside faces. For a cuboid, use 2(lw + lh + wh). For a triangular prism, add the areas of its two triangular ends and three rectangular faces. Show your working and give answers in square units.

Worked example: A cuboid measuring 4 cm × 3 cm × 2 cm has surface area 2(12 + 8 + 6) = 52 cm².

1. Find the surface area of a cuboid measuring 5 cm × 3 cm × 2 cm.

2. A triangular prism has two triangular ends, each with base 4 cm and perpendicular height 3 cm. The three rectangular faces have areas 20 cm², 20 cm² and 24 cm². Find the total surface area.

3. Find the surface area of a cube with side length 4 cm.

Answer Key

Activity 1: 1. 72° ; 2. 118° ; 3. 116° ; 4. 43°

Activity 2: 1. 540° ; 2. 45° ; 3. 108° ; 4. 8 sides

Activity 3: 1. 25.12 cm ; 2. 31.4 cm ; 3. 78.5 cm² ; 4. 50.24 cm²

Activity 4: 1. 36 cm³ ; 2. 48 cm³ ; 3. 3 cm ; 4. 84 cm³

Activity 5: 1. 62 cm² ; 2. 76 cm² ; 3. 96 cm²