Geometry Worksheet — GCSE — Intermediate

Geometry worksheet for Key Stage 4 / GCSE (Ages 14-16). Intermediate level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.

Maths•Key Stage 4 / GCSE (Ages 14-16)•Geometryintermediate

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Exploring Geometry: Intermediate Challenges

Key Stage 4 / GCSE (Ages 14-16) - Intermediate Level

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Instructions: This worksheet focuses on intermediate geometry concepts, including problem-solving, data analysis, and extended writing. Each activity is designed to enhance your understanding and application of geometric principles.

Angle Identification

Identify the type of each angle shown below. Write your answer in the box provided. Consider whether each angle is acute, right, obtuse, or straight.

Calculating Area and Perimeter

Calculate the area and perimeter for each shape given below. Use the formulas for rectangles and triangles to find your answers.

1. Rectangle: Length = 8 cm, Width = 5 cm

Area: cm²

Perimeter: cm

2. Triangle: Base = 6 cm, Height = 4 cm

Area: cm²

Perimeter (assuming an equilateral triangle): cm

Pythagorean Theorem Application

Use the Pythagorean theorem to find the missing side of each right triangle. Show all calculations clearly in the space provided.

1. a = 3 cm, b = 4 cm, c = ?

c = cm

2. a = ?, b = 5 cm, c = 13 cm

a = cm

Volume of 3D Shapes

Calculate the volume of each 3D shape using the given dimensions. Use the formula for the volume of a rectangular prism: Volume = Length × Width × Height.

1. Length = 4 cm, Width = 3 cm, Height = 5 cm

Volume: cm³

2. Length = 7 cm, Width = 2 cm, Height = 6 cm

Volume: cm³

Data Analysis: Geometric Shapes

Analyse the data in the table and answer the questions below. Consider the properties of each shape when answering.

Shape	Sides	Vertices	Angles
Triangle	3	3	3
Square	4	4	4
Rectangle	4	4	4
Hexagon	6	6	6

1. Which shape has the most sides?

2. How many angles does a square have?

3. Compare the number of sides between a triangle and a hexagon.

Transformations: Reflection and Rotation

Describe the transformation that maps shape A to shape B for each pair. Consider both reflection and rotation transformations.

1. Shape A is reflected over the y-axis to become Shape B. Describe this transformation:

2. Shape A is rotated 90 degrees clockwise to become Shape B. Describe this transformation:

Extended Writing: Geometric Proofs

Write a detailed essay proving that the sum of the interior angles of a triangle is always 180 degrees. Use diagrams and algebraic expressions to support your proof.

Prove that the sum of the interior angles of a triangle is 180 degrees. Include diagrams and algebraic expressions in your explanation. [10 marks]